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Tesis sobre el tema "Mirror symmetry"

Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 25 de julio de 2025

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1

Branco, Lucas Castello. "Higgs bundles, Lagrangians and mirror symmetry." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:612325bd-6a7f-4d74-a85c-426b73ff7a14.

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Let Σ be a compact Riemann surface of genus g ≥ 2. This thesis is dedicated to the study of certain loci of the Higgs bundle moduli space. After recalling basic facts in the first chapter about G-Higgs bundles for a reductive group G, we begin the first part of the work, which deals with Higgs bundles for the real forms G<sub>0</sub> = SU* (2m), SO* (4m), and Sp(m, m) of G = SL(2m, C), SO(4m, C) and Sp(4m, C), respectively. The second part of the thesis deals with the Gaiotto Lagrangian. Motivated by mirror symmetry, we give a detailed description of the fibres of the G-Hitchin fibration conta

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2

Mertens, Adrian. "Mirror Symmetry in the presence of Branes." Diss., lmu, 2011. http://nbn-resolving.de/urn:nbn:de:bvb:19-135464.

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3

Gu, Wei. "Gauged Linear Sigma Model and Mirror Symmetry." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/90892.

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This thesis is devoted to the study of gauged linear sigma models (GLSMs) and mirror symmetry. The ﬁrst chapter of this thesis aims to introduce some basics of GLSMs and mirror symmetry. The second chapter contains the author's contributions to new exact results for GLSMs obtained by applying supersymmetric localization. The ﬁrst part of that chapter concerns supermanifolds. We use supersymmetric localization to show that A-twisted GLSM correlation functions for certain supermanifolds are equivalent to corresponding Atwisted GLSM correlation functions for hypersurfaces. The second part of that

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4

Perevalov, Eugene V. "Type II/heterotic duality and mirror symmetry /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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5

Rossi, Paolo. "Symplectic Topology, Mirror Symmetry and Integrable Systems." Doctoral thesis, SISSA, 2008. http://hdl.handle.net/11577/3288900.

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Using Sympelctic Field Theory as a computational tool, we compute Gromov-Witten theory of target curves using gluing formulas and quantum integrable systems. In the smooth case this leads to a relation of the results of Okounkov and Pandharipande with the quantum dispersionless KdV hierarchy, while in the orbifold case we prove triple mirror symmetry between GW theory of target P^1 orbifolds of positive Euler characteristic, singularity theory of a class of polynomials in three variables and extended affine Weyl groups of type ADE.

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6

Rossi, Paolo. "Symplectic Topology, Mirror Symmetry and Integrable systems." Doctoral thesis, SISSA, 2008. http://hdl.handle.net/20.500.11767/4193.

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The plan of the work is the following: ² In Chapter 1 we recall, basically from [16] and [14], the ideas and methods of Symplectic Field Theory. Our review will focus on the algebraic structure arising from topology, more than on the geometry underlying it. In particular we de¯ne the SFT analogue of the Gromov-Witten potential as an element in some graded Weyl algebra and consider its properties (grading, master equations, semiclassical limit). We then stress (following [18]) how this algebraic structure allows the appearence of a system of commuting di®erential operators (on the homolo

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7

Krefl, Daniel. "Real Mirror Symmetry and The Real Topological String." Diss., lmu, 2009. http://nbn-resolving.de/urn:nbn:de:bvb:19-102832.

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8

Williams, Matthew Michael. "Mirror Symmetry for Non-Abelian Landau-Ginzburg Models." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/8560.

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We consider Landau-Ginzburg models stemming from non-abelian groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group G*, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors in general.

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9

Ueda, Kazushi. "Homological mirror symmetry for toric del Pezzo surfaces." 京都大学 (Kyoto University), 2006. http://hdl.handle.net/2433/144153.

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Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(理学)<br>甲第12069号<br>理博第2963号<br>新制||理||1443(附属図書館)<br>23905<br>UT51-2006-J64<br>京都大学大学院理学研究科数学・数理解析専攻<br>(主査)助教授河合俊哉, 教授齋藤恭司, 教授柏原正樹<br>学位規則第4条第1項該当

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10

Kadir, Shabnam Nargis. "The arithmetic of Calabi-Yau manifolds and mirror symmetry." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403756.

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11

Petracci, Andrea. "On Mirror Symmetry for Fano varieties and for singularities." Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/55877.

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In this thesis we discuss some aspects of Mirror Symmetry for Fano varieties and toric singularities. We formulate a conjecture that relates the quantum cohomology of orbifold del Pezzo surfaces to a power series that comes from Fano polygons. We verify this conjecture in some cases, in joint work with A. Oneto. We generalise the Altmann–Mavlyutov construction of deformations of toric singularities: from Minkowski sums of polyhedra we construct deformations of affine toric pairs. Moreover, we propose an approach to the study of deformations of Gorenstein toric singularities of dimension 3 in t

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12

Bott, Christopher James. "Mirror Symmetry for K3 Surfaces with Non-symplectic Automorphism." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/7456.

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Mirror symmetry is the phenomenon, originally discovered by physicists, that Calabi-Yau manifolds come in dual pairs, with each member of the pair producing the same physics. Mathematicians studying enumerative geometry became interested in mirror symmetry around 1990, and since then, mirror symmetry has become a major research topic in pure mathematics. One important problem in mirror symmetry is that there may be several ways to construct a mirror dual for a Calabi-Yau manifold. Hence it is a natural question to ask: when two different mirror symmetry constructions apply, do they agree?We sp

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13

Matessi, Diego. "Constructions of Calabi Yau metrics and of special Lagrangian submanifolds." Thesis, University of Warwick, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246770.

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14

Alim, Murad. "Mirror Symmetry, Toric Branes and Topological String Amplitudes as Polynomials." Diss., lmu, 2009. http://nbn-resolving.de/urn:nbn:de:bvb:19-103416.

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15

Hartmann, Heinrich [Verfasser]. "Mirror symmetry and stability conditions on K3 surfaces / Heinrich Hartmann." Bonn : Universitäts- und Landesbibliothek Bonn, 2011. http://d-nb.info/1016152949/34.

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16

Yang, Wenzhe. "The arithmetic geometry of mirror symmetry and the conifold transition." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:e55a7b22-a268-4c57-9d98-c0547ecdcef9.

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The central theme of this thesis is the application of mirror symmetry to the study of the arithmetic geometry of Calabi-Yau threefolds. It formulates a conjecture about the properties of the limit mixed Hodge structure at the large complex structure limit of an arbitrary mirror threefold, which is supported by a two-parameter example of a self-mirror Calabi-Yau threefold. It further studies the connections between this conjecture with Voevodsky's mixed motives. This thesis also studies the connections between the conifold transition and Beilinson's conjecture on the values of the L-functions

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17

Prince, Thomas. "Applications of mirror symmetry to the classification of Fano varieties." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/43374.

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In this dissertation we discuss two new constructions of Fano varieties, each directly inspired by ideas in Mirror Symmetry. The first recasts the Fanosearch program (Coates--Corti--Kasprzyk et al.) for surfaces in terms of a construction related to the SYZ conjecture. In particular we construct Q-Gorenstein smoothings of toric varieties via an application of the Gross-Siebert algorithm to certain affine manifolds. We recover the theory of combinatorial mutation, which plays a central role in the Fanosearch program, from these affine manifolds. Combining this construction and the work of Gross

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18

Borokhov, Vadim Aleksandrovich Kapustin Anton N. "Monopole operators and mirror symmetry in three-dimensional gauge theories /." Diss., Pasadena, Calif. : California Institute of Technology, 2004. http://resolver.caltech.edu/CaltechETD:etd-04062004-015855.

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19

Sigrist, Norbert. "First-order design of mirror systems with no axial symmetry." Diss., The University of Arizona, 1999. http://hdl.handle.net/10150/284660.

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All-reflective imaging systems that are asymmetrical and eccentric have the advantage of providing more degrees of freedom to improve image quality. A disadvantage of these asymmetrical imaging systems is that they suffer from asymmetric mapping. This asymmetric mapping manifests itself mainly in the presence of keystone distortion and anamorphism. Due to the increase in degrees of freedom, the complexity of such systems escalates; thus, the designer is confronted with the difficult task of determining optimal starting points. This work addresses several first-order aspects of the design and c

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20

Johnson, Jared Drew. "An Algebra Isomorphism for the Landau-Ginzburg Mirror Symmetry Conjecture." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2793.

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Landau-Ginzburg mirror symmetry takes place in the context of affine singularities in CN. Given such a singularity defined by a quasihomogeneous polynomial W and an appropriate group of symmetries G, one can construct the FJRW theory (see [3]). This construction fills the role of the A-model in a mirror symmetry proposal of Berglund and H ubsch [1]. The conjecture is that the A-model of W and G should match the B-model of a dual singularity and dual group (which we denote by WT and GT). The B-model construction is based on the Milnor ring, or local algebra, of the singularity. We verify this c

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21

Zhang, Xiangwen 1984. "Mean curvature flow for Lagrangian submanifolds with convex potentials." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=111593.

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In recent years symplectic geometry and symplectic topology have grown to large subbranches in mathematics and had a great impact on other areas in mathematics. When interested in geometry, a geometer always considers geometric structures that arise on immersed submanifolds. In symplectic geometry there is a distinguished class of immersions, known as Lagrangian submanifolds . In particular, minimal Lagrangian submanifolds, called special Lagrangians, are very important in mirror symmetry. Lagrangian mean curvature flow is an important example of Lagrangian deformation. From which we can get t

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22

Mukai, Daichi. "Mirror symmetry of nonabelian Landau-Ginzburg orbifolds with loop type potentials." Kyoto University, 2020. http://hdl.handle.net/2433/253068.

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23

Pumperla, Max [Verfasser], and Bernd [Akademischer Betreuer] Siebert. "Unifying Constructions in Toric Mirror Symmetry / Max Pumperla. Betreuer: Bernd Siebert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2012. http://d-nb.info/1026332966/34.

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24

Böhm, Janko [Verfasser], and Frank-Olaf [Akademischer Betreuer] Schreyer. "Mirror symmetry and tropical geometry / Janko Böhm. Betreuer: Frank-Olaf Schreyer." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2011. http://d-nb.info/1051094968/34.

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25

Lu, Wenxuan. "Instanton correction, wall crossing and mirror symmetry of Hitchin's moduli spaces." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/67809.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 205-210).<br>We study two instanton correction problems of Hitchin's moduli spaces along with their wall crossing formulas. The hyperkahler metric of a Hitchin's moduli space can be put into an instanton-corrected form according to physicists Gaiotto, Moore and Neitzke. The problem boils down to the construction of a set of special coordinates which can be constructed as Fock-Goncharov coordinates associated with foliations of q

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26

Vaintrob, Dmitry. "Mirror symmetry and the K theory of a p-adic group." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104578.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 59-61).<br>Let G be a split, semisimple p-adic group. We construct a derived localization functor Loc : ... from the compactified category of [BK2] associated to G to the category of equivariant sheaves on the Bruhat-Tits building whose stalks have finite-multiplicity isotypic components as representations of the stabilizer. Our construction is motivated by the "coherent-constructible correspondence" functor in toric mirr

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27

Sheridan, Nicholas (Nicholas James). "Homological mirror symmetry for a Calabi-Yau hypersurface in projective space." Thesis, Massachusetts Institute of Technology, 2012. http://hdl.handle.net/1721.1/73374.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 365-369).<br>This thesis is concerned with Kontsevich's Homological Mirror Symmetry conjecture. In Chapter 1, which is based on [1], we consider the n-dimensional pair of pants, which is defined to be the complement of n + 2 generic hyperplanes in CPn. The pair of pants is conjectured to be mirror to the Landau-Ginzburg model (Cn+2 , W), where W = z1...zn+2 We construct an immersed Lagrangian sphere in the pair of pants, and sho

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28

MAGID, DIANE ALEXIS. "FRAMES OF REFERENCE, THE PERCEPTION OF SYMMETRY AND THE MIRROR ILLUSION (ENANTIOMORPHS)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/188154.

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The relationship between symmetry and apparent reversals of enantiomorphic (mirror-reflected) objects was investigated. Subjects were presented with a series of standard and enantiomorphic books with various structural symmetries. The object directions (top-front-right) assigned to standard books were compared with the directions assigned to their enantiomorphs and the axes of apparent reversal determined. The primary finding was that apparent reversals were not limited to the left-right dimension. Reversals of top-bottom and front-back were also obtained. In most cases, apparent reversals occ

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29

Barrott, Lawrence Jack. "Convergence of the mirror to a rational elliptic surface." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/285007.

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The construction introduced by Gross, Hacking and Keel in [28] allows one to construct a mirror family to (S, D) where S is a smooth rational projective surface and D a certain type of Weil divisor supporting an ample or anti-ample class. To do so one constructs a formal smoothing of a singular variety they call the n-vertex. By arguments of Gross, Hacking and Keel one knows that this construction can be lifted to an algebraic family if the intersection matrix for D is not negative semi-definite. In the case where the intersection matrix is negative definite the smoothing exists in a formal ne

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30

Rainville, Stéphane Jean Michel. "The spatial mechanisms mediating the perception of mirror symmetry in human vision /." Thesis, McGill University, 1999. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=36688.

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The present thesis reports psychophysical and modeling studies on the spatial properties of visual mechanisms mediating the perception of mirror symmetry in human vision. In a first set of experiments, patterns were filtered for power spectra that decayed with spatial frequency according to variable slopes. Results revealed that symmetry detection is optimal if contrast energy is roughly equated across log-frequency bands (i.e. 1/f2) and that, under such conditions, spatial scales contribute equally and independently to symmetry perception. In a second study, random-noise patterns were filtere

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31

Basalaev, Alexey [Verfasser]. "Mirror symmetry for simple elliptic singularities with a group action / Alexey Basalaev." Hannover : Technische Informationsbibliothek und Universitätsbibliothek Hannover (TIB), 2015. http://d-nb.info/1073604454/34.

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32

Mertens, Adrian [Verfasser], and Christian [Akademischer Betreuer] Römelsberger. "Mirror Symmetry in the presence of Branes / Adrian Mertens. Betreuer: Christian Römelsberger." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2011. http://d-nb.info/1016172877/34.

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33

Rainville, Stéphane Jean Michel. "The spatial mechanisms mediating the perception of mirror symmetry in human vision." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ64650.pdf.

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34

Buchholz, Arne Verfasser], and Hannah [Akademischer Betreuer] [Markwig. "Tropical covers, moduli spaces & mirror symmetry / Arne Buchholz. Betreuer: Hannah Markwig." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2014. http://d-nb.info/1060715953/34.

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35

Jost, Jan Niklas [Verfasser], and Thomas [Akademischer Betreuer] Reichelt. "Mirror Symmetry for Del Pezzo Surfaces / Jan Niklas Jost ; Betreuer: Thomas Reichelt." Heidelberg : Universitätsbibliothek Heidelberg, 2021. http://d-nb.info/1227711492/34.

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36

Jost, Jan [Verfasser], and Thomas [Akademischer Betreuer] Reichelt. "Mirror Symmetry for Del Pezzo Surfaces / Jan Niklas Jost ; Betreuer: Thomas Reichelt." Heidelberg : Universitätsbibliothek Heidelberg, 2021. http://d-nb.info/1227711492/34.

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37

Smorenburg, Ana Renée Pascale. "Mirror (a)symmetry? : visuo-proprioceptive interactions in individuals with spastic hemiparetic cerebral palsy." Thesis, Manchester Metropolitan University, 2012. http://e-space.mmu.ac.uk/314042/.

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The work presented in this thesis aimed to get more insight into the previously reported positive effects of mirror visual feedback in children with spastic hemiparetic cerebral palsy (SHCP) and into visuo-proprioceptive interactions in children and adolescents with SHCP during goal-directed matching tasks. Individuals with SHCP have unilateral motor impairments that hamper them in accurate movement performance. In conjunction with the motor problems, these individuals experience sensory problems. The first study in this thesis (chapter two) found that mirror visual feedback of the impaired ar

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38

Huang, Yu-Chien Ph D. Massachusetts Institute of Technology. "Elliptic fibrations among toric hypersurface Calabi-Yau manifolds and mirror symmetry of fibrations." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/124593.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2019<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 245-255).<br>In this thesis, we investigate the prevalence of elliptic and genus one fibrations among toric hypersurface Calabi-Yau three folds by (1) constructing explicitly elliptically fibered Calabi-Yau threefolds with large Hodge numbers using Weierstrass model techniques motivated by F-theory, and comparing the Tate-tuned Wierstrass model set with the set of Calabi-Yau threefolds constructed using toric hypersurface meth

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39

Francis, Amanda. "New Computational Techniques in FJRW Theory with Applications to Landau Ginzburg Mirror Symmetry." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3265.

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Mirror symmetry is a phenomenon from physics that has inspired a lot of interesting mathematics. In the Landau-Ginzburg setting, we have two constructions, the A and B models, which are created based on a choice of an affine singularity with a group of symmetries. Both models are vector spaces equipped with multiplication and a pairing (making them Frobenius algebras), and they are also Frobenius manifolds. We give a result relating stabilization of singularities in classical singularity to its counterpart in the Landau-Ginzburg setting. The A model comes from so-called FJRW theory and can be

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40

Jones, Daniel M. "A convergent beam electron diffraction study of some rare-earth perovskite oxides /." Connect to this title, 2007. http://theses.library.uwa.edu.au/adt-WU2008.0057.

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41

Brown, Matthew Robert. "Construction and Isomorphism of Landau-Ginzburg B-Model Frobenius Algebras." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/5652.

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Landau-Ginzburg Mirror Symmetry provides for the construction of two algebraic objects, called the A- and B-models. Special cases of these models–constructed using invertible polynomials and abelian symmetry groups–are well understood. In this thesis, we consider generalizations of the B-model, and specifically address the associativity of the multiplication in these models. We also prove an explicit B-model isomorphism for a class of polynomials in three variables.

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42

Cordner, Nathan James. "Isomorphisms of Landau-Ginzburg B-Models." BYU ScholarsArchive, 2016. https://scholarsarchive.byu.edu/etd/5882.

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Landau-Ginzburg mirror symmetry predicts isomorphisms between graded Frobenius algebras (denoted A and B) that are constructed from a nondegenerate quasihomogeneous polynomial W and a related group of symmetries G. In 2013, Tay proved that given two polynomials W1, W2 with the same quasihomogeneous weights and same group G, the corresponding A-models built with (W1, G) and (W2, G) are isomorphic. An analogous theorem for isomorphisms between orbifolded B-models remains to be found. This thesis investigates isomorphisms between B-models using polynomials in two variables in search of such a th

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43

Argüz, Nurömür Hülya [Verfasser], and Bernd [Akademischer Betreuer] Siebert. "Log geometric techniques for open invariants in mirror symmetry / Nurömür Hülya Argüz ; Betreuer: Bernd Siebert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2017. http://d-nb.info/1123729506/34.

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44

Argüz, Nurömür Hülya Verfasser], and Bernd [Akademischer Betreuer] [Siebert. "Log geometric techniques for open invariants in mirror symmetry / Nurömür Hülya Argüz ; Betreuer: Bernd Siebert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2017. http://nbn-resolving.de/urn:nbn:de:gbv:18-82774.

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45

Jones, Daniel M. "A convergent beam electron diffraction study of some rare-earth perovskite oxides." University of Western Australia. School of Physics, 2008. http://theses.library.uwa.edu.au/adt-WU2008.0057.

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This work describes detailed convergent beam electron diffraction (CBED) studies of GdAlO3 and LaAlO3 perovskites. CBED patterns tilted away from major zone axes have been found to have high sensitivity to the presence of mirror or glide mirror symmetry. Such patterns confirm to high accuracy that the space group of GdAlO3 is orthorhombic, Pnma. Tilted patterns from this well characterised structure also serve as benchmarks against which similar patterns may be compared. In the case of LaAlO3, tilted patterns enable the space group to be confirmed as rhombohedral R3c, previously claimed to be

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46

Wu, Ruoxu. "Notes on Some (0,2) Supersymmetric Theories in Two Dimensions." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/77921.

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This thesis is devoted to a discussion of two-dimensional theories with (0,2) supersymmetry. Examples of two-dimensional (0,2) gauged linear sigma models (GLSMs) are constructed for various spaces including Grassmannians, complete intersections in Grassmannians, and non-complete intersections such as Pfaffians. Generalizations of (2,2) Toda dual theories to (0,2) Toda-like theories are also discussed and some examples are given, including products of projective spaces and del Pezzo surfaces. Correlation functions are computed to show the examples are the correct mirror models.<br>Ph. D.

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47

Pavanelli, Simone. "Mirror symmetry for a two parameter family of Calabi-Yau three-folds with Euler characteristic 0." Thesis, University of Warwick, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.396954.

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48

Goldner, Christoph Jan [Verfasser]. "Enumerative aspects of Tropical Geometry : Curves with cross-ratio constraints and Mirror Symmetry / Christoph Jan Goldner." Tübingen : Universitätsbibliothek Tübingen, 2021. http://d-nb.info/1233678248/34.

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49

Merrell, Evan D. "A Maple Program for Computing Landau-Ginzburg A- and B-Models and an Exploration of Mirror Symmetry." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3322.

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Mirror symmetry has been a significant area of research for geometry and physics for over two decades. Berglund and Hubsch proposed that for a certain family of singularities W, the so called "transposed" singularity WT should be the mirror partner of W. cite{BH} The techniques for constructing the orbifold LG models to test this conjecture were developed by FJR in cite{FJR} with a cohomological field theory generalized from the study of r-spin curves. The duality of LG A- and B-models became more elaborate when Krawitz cite{Krawitz} generalized the Intriligator-Vafa orbifold B-model to includ

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Comparin, Paola. "Symétrie miroir et fibrations elliptiques spéciales sur les surfaces K3." Thesis, Poitiers, 2014. http://www.theses.fr/2014POIT2281/document.

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Une surface K3 est une surface X complexe compacte projective lisse qui a fibré canonique trivial et h0;1(X) = 0. Dans cette thèse on s'intéresse à deux problèmes pour ces surfaces. D'abord on considère des surfaces K3 obtenues comme recouvrement double de P2 ramifié le long d'une sextique. On classifie les fibrations elliptiques sur ces surfaces et leur groupe de Mordell-Weil, c'est-à-dire le groupe des sections. Vu que une section de 2-torsion définit une involution de la surface (dite involution de van Geemen-Sarti), alors en classifiant les fibrations et les section de 2-torsion on obtient

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