Academic literature on the topic 'Compactification of moduli spaces'

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Journal articles on the topic "Compactification of moduli spaces"

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Toda, Yukinobu. "Moduli spaces of stable quotients and wall-crossing phenomena." Compositio Mathematica 147, no. 5 (2011): 1479–518. http://dx.doi.org/10.1112/s0010437x11005434.

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AbstractThe moduli space of holomorphic maps from Riemann surfaces to the Grassmannian is known to have two kinds of compactifications: Kontsevich’s stable map compactification and Marian–Oprea–Pandharipande’s stable quotient compactification. Over a non-singular curve, the latter moduli space is Grothendieck’s Quot scheme. In this paper, we give the notion of ‘ ϵ-stable quotients’ for a positive real number ϵ, and show that stable maps and stable quotients are related by wall-crossing phenomena. We will also discuss Gromov–Witten type invariants associated to ϵ-stable quotients, and investigate them under wall crossing.
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Martens, Johan, and Michael Thaddeus. "Compactifications of reductive groups as moduli stacks of bundles." Compositio Mathematica 152, no. 1 (2015): 62–98. http://dx.doi.org/10.1112/s0010437x15007484.

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Let $G$ be a split reductive group. We introduce the moduli problem of bundle chains parametrizing framed principal $G$-bundles on chains of lines. Any fan supported in a Weyl chamber determines a stability condition on bundle chains. Its moduli stack provides an equivariant toroidal compactification of $G$. All toric orbifolds may be thus obtained. Moreover, we get a canonical compactification of any semisimple $G$, which agrees with the wonderful compactification in the adjoint case, but which in other cases is an orbifold. Finally, we describe the connections with Losev–Manin’s spaces of weighted pointed curves and with Kausz’s compactification of $GL_{n}$.
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Greb, Daniel, Julius Ross, and Matei Toma. "Moduli of vector bundles on higher-dimensional base manifolds — Construction and variation." International Journal of Mathematics 27, no. 07 (2016): 1650054. http://dx.doi.org/10.1142/s0129167x16500543.

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We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson–Uhlenbeck compactification and explain how to use moduli spaces of quiver representations to show that Gieseker–Maruyama moduli spaces with respect to two different chosen polarizations are related via Thaddeus-flips through other “multi-Gieseker”-moduli spaces of sheaves. Moreover, as a new result, we show the existence of a natural morphism from a multi-Gieseker moduli space to the corresponding Donaldson–Uhlenbeck moduli space.
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Katić, Jelena. "Compactification of Mixed Moduli Spaces in Morse-Floer Theory." Rocky Mountain Journal of Mathematics 38, no. 3 (2008): 923–39. http://dx.doi.org/10.1216/rmj-2008-38-3-923.

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Scavia, Federico. "Rational Picard Group of Moduli of Pointed Hyperelliptic Curves." International Mathematics Research Notices 2020, no. 21 (2020): 8027–56. http://dx.doi.org/10.1093/imrn/rnaa003.

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Scattone, Francesco. "On the compactification of moduli spaces for algebraic 𝐾3 surfaces". Memoirs of the American Mathematical Society 70, № 374 (1987): 0. http://dx.doi.org/10.1090/memo/0374.

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BHOSLE, USHA, INDRANIL BISWAS, and JACQUES HURTUBISE. "GRASSMANNIAN-FRAMED BUNDLES AND GENERALIZED PARABOLIC STRUCTURES." International Journal of Mathematics 24, no. 12 (2013): 1350090. http://dx.doi.org/10.1142/s0129167x13500900.

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We build compact moduli spaces of Grassmannian-framed bundles over a Riemann surface, essentially replacing a group by a bi-equivariant compactification. We do this both in the algebraic and symplectic settings, and prove a Hitchin–Kobayashi correspondence between the two. The spaces are universal spaces for parabolic bundles (in the sense that all of the moduli can be obtained as quotients), and the reduction to parabolic bundles commutes with the correspondence. An analogous correspondence is outlined for the generalized parabolic bundles of Bhosle.
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Camere, Chiara. "Some remarks on moduli spaces of lattice polarized holomorphic symplectic manifolds." Communications in Contemporary Mathematics 20, no. 04 (2018): 1750044. http://dx.doi.org/10.1142/s0219199717500444.

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We construct quasi-projective moduli spaces of [Formula: see text]-general lattice polarized irreducible holomorphic symplectic manifolds. Moreover, we study their Baily–Borel compactification and investigate a relation between one-dimensional boundary components and equivalence classes of rational Lagrangian fibrations defined on mirror manifolds.
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SABRA, W. A., S. THOMAS, and N. VANEGAS. "SPECIAL GEOMETRY AND TWISTED MODULI IN ORBIFOLD THEORIES WITH CONTINUOUS WILSON LINES." Modern Physics Letters A 11, no. 16 (1996): 1307–16. http://dx.doi.org/10.1142/s0217732396001314.

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Target space duality symmetries, which acts on Kähler and continuous Wilson line moduli, of a ZN (N≠2) two-dimensional subspace of the moduli space of orbifold compactification are modified to include twisted moduli. These spaces described by the cosets [Formula: see text] are special Kähler, a fact which is exploited in deriving the extension of tree level duality transformation to include higher orders of the twisted moduli. Also, restrictions on these higher order terms are derived.
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Lekili, Yankı, та Alexander Polishchuk. "A modular compactification of ℳ1,n from A∞-structures". Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, № 755 (2019): 151–89. http://dx.doi.org/10.1515/crelle-2017-0015.

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AbstractWe show that a certain moduli space of minimal A_{\infty}-structures coincides with the modular compactification {\overline{\mathcal{M}}}_{1,n}(n-1) of \mathcal{M}_{1,n} constructed by Smyth in [26]. In addition, we describe these moduli spaces and the universal curves over them by explicit equations, prove that they are normal and Gorenstein, show that their Picard groups have no torsion and that they have rational singularities if and only if n\leq 11.
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Dissertations / Theses on the topic "Compactification of moduli spaces"

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Deopurkar, Anand. "Alternate Compactifications of Hurwitz Spaces." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10308.

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We construct several modular compactifications of the Hurwitz space \(H^d_{g/h}\) of genus g curves expressed as d-sheeted, simply branched covers of genus h curves. They are obtained by allowing the branch points of the cover to collide to a variable extent, generalizing the spaces of twisted admissible covers of Abramovich, Corti, and Vistoli. The resulting spaces are very well-behaved if d is small or if relatively few collisions are allowed. In particular, for d = 2 and 3, they are always well-behaved. For d = 2, we recover the spaces of hyperelliptic curves of Fedorchuk. For d = 3, we obtain new birational models of the space of triple covers. We describe in detail the birational geometry of the spaces of triple covers of \(P^1\) with a marked fiber. In this case, we obtain a sequence of birational models that begins with the space of marked (twisted) admissible covers and proceeds through the following transformations: (1) sequential contractions of the boundary divisors, (2) contraction of the hyperelliptic divisor, (3) sequential flips of the higher Maroni loci, (4) contraction of the Maroni divisor (for even g). The sequence culminates in a Fano variety in the case of even g, which we describe explicitly, and a variety fibered over \(P^1\) with Fano fibers in the case of odd g.<br>Mathematics
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Walton, Mark 1960. "Two scale compactification of the E(8)xE(8) heterotic string." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75346.

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A simple two scale compactification scheme for the E(8) x E(8) heterotic string is studied. The internal space used is a direct product of two compact spaces, each with its own length scale. Compactification on the smaller 4-dimensional (4d) manifold is carried out to obtain 6d theories with simple supersymmetry (SUSY). Assuming the background torsion vanishes, we show that this manifold must be K3. Compactification on K3 is studied in detail. Also analyzed are the two possible torsion-free compactifications on the orbifold K3$ sp prime$ (the limit of the manifold K3). The compactification from 6d to 4d on the larger scale 2d manifold results in Grand Unified Theories (GUT's) with broken SUSY. We show that it is not possible to generate a realistic theory using our scheme. Strings exclude what is conceivable from the perspective of point field theories: getting a realistic GUT from a 6d theory with simple SUSY.
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Daniel, Panizo. "Review of compact spaces for type IIA/IIB theories and generalised fluxes." Thesis, Uppsala universitet, Institutionen för fysik och astronomi, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-384227.

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In the present project we study compactifications of type IIA/IIB string theories on toroidal orbifolds. We present the moduli space for N=1 four-dimensional reductions and its topological properties. To fix the value of all moduli, we will construct the most general holomorphic superpotential W using a set of T-dual iterations for the fluxes. Using a 3-torus toy-model, we will give an introductory description to the background of these generalised fluxes.
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Shao, Yijun. "A Compactification of the Space of Algebraic Maps from P^1 to a Grassmannian." Diss., The University of Arizona, 2010. http://hdl.handle.net/10150/194715.

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Let Md be the moduli space of algebraic maps (morphisms) of degree d from P^1 to a fixed Grassmannian. The main purpose of this thesis is to provide an explicit construction of a compactification of Md satisfying the following property: the compactification is a smooth projective variety and the boundary is a simple normal crossing divisor. The main tool of the construction is blowing-up. We start with a smooth compactification given by Quot scheme, which we denote by Qd. The boundary Qd\Md is singular and of high codimension. Next, we give a filtration of the boundary Qd\Md by closed subschemes: Zd,0 subset Zd,1 subset ... Zd,d-1=Qd\Md. Then we blow up the Quot scheme Qd along these subschemes succesively, and prove that the final outcome is a compactification satisfying the desired properties. The proof is based on the key observation that each Zd,r has a smooth projective variety which maps birationally onto it. This smooth projective variety, denoted by Qd,r, is a relative Quot scheme over the Quot-scheme compactification Qr for Mr. The map from Qd,r to Zd,r is an isomorphism when restricted to the preimage of Zd,r\ Zd,r-1. With the help of the Qd,r's, one can show that the final outcome of the successive blowing-up is a smooth compactification whose boundary is a simple normal crossing divisor.
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Boes, Felix Jonathan [Verfasser]. "On moduli spaces of Riemann surfaces : new generators in their unstable homology and the homotopy type of their harmonic compactification / Felix Jonathan Boes." Bonn : Universitäts- und Landesbibliothek Bonn, 2018. http://d-nb.info/1170778070/34.

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Goluboff, Justin Ross. "Genus Six Curves, K3 Surfaces, and Stable Pairs:." Thesis, Boston College, 2020. http://hdl.handle.net/2345/bc-ir:108715.

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Thesis advisor: Maksym Fedorchuk<br>A general smooth curve of genus six lies on a quintic del Pezzo surface. In [AK11], Artebani and Kondō construct a birational period map for genus six curves by taking ramified double covers of del Pezzo surfaces. The map is not defined for special genus six curves. In this dissertation, we construct a smooth Deligne-Mumford stack P₀ parametrizing certain stable surface-curve pairs which essentially resolves this map. Moreover, we give an explicit description of pairs in P₀ containing special curves<br>Thesis (PhD) — Boston College, 2020<br>Submitted to: Boston College. Graduate School of Arts and Sciences<br>Discipline: Mathematics
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Hatter, Luke. "Cohomology of compactifications of moduli spaces of stable bundles over a Riemann surface." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.389176.

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Morzadec, Thomas. "Compactification géométrique de l'espace de modules des structures de demi-translation sur une surface." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS225/document.

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L'objectif de la thèse est de construire une compactification géométrique de l'espace des structures de demi-translation sur une surface S compacte, connexe, orientable, de genre au moins égal à 2. Il s’inscrit dans le très large thème d’étude des déformations de structures géométriques sur les surfaces. Une structure de demi-translation sur S est une métrique localement euclidienne (de courbure constante nulle) sur S, avec des singularités coniques d'angles k pi, avec k un entier et k&gt;2, telle que l'holonomie de tout lacet lisse de S, disjoint des singularités, est Id ou -Id.Je définis l'ensemble des structures mixtes sur S, qui sont des structures arborescentes (au sens de Drutu-Sapir), équivariantes par le groupe fondamentalde S et CAT(0), obtenues par recollement de pièces par des arêtes, éventuellement réduites à des points, telles que l'espace obtenu par écrasement des pièces est un arbre réel simplicial (la plupart des arêtes ont une longueur non nulle), et les pièces sont ou bien des arbres réels, ou bien des revêtements universels de sous-surfaces (ouvertes) de S, munies de structures de demi-translation. Je munis l'espace Mix(Sigma) des (classes d'isométries équivariantes par le groupe fondamental de S) de structures mixtes sur S d'une topologie géométrique naturelle, appelée topologie de Gromov équivariante. Je montre alors, par des techniques d'ultralimites à la Gromov, que l'espace Flat(S) des (classes d'isotopie de) structures de demi-translation sur S, identifié à l’ensemble des structures de demi-translation équivariantes par le groupe fondamental de S sur le revêtement universel de S, est un ouvert dense de Mix(S), et que le projectifié PMix(S), muni de la topologie quotient, est compact. Le projectifié PMix(S) est donc une compactification du projectifié PFlat(S) de l'espace Flat(S) (qui s'identifie à l'espace des structure de demi-translation d'aire 1 sur S)<br>The goal of this thesis is to build a geometric compactification of the space of half-translation structures on a connected, compact surface S, with genus at least 2. It is a part of the wide thema of study of the deformations of metric structures on surfaces.A half-translation structure on S is a locally euclidean metric (with null constant curvature) on S, with conical singularities of angles k pi, with k an integer and k&gt;2, such that the holonomy of every smooth curve of S, disjoint from the singularities, is contained in Id or -Id.I define the set of mixed structures on S, which are tree-graded spaces (in the sense of Drutu-Sapir), equivariant by the fundamental group of S and CAT(0), obtained by gluing some pieces by some edges, possibly reduced to a point, such that the space obtained by replacing the pieces by some points is a simplicialtree (most edges have a positive length), and the pieces are either some trees or some universal covers of (open) subsurfaces of S endowed with a half-translation structures. I endow the space Mix(S) of (classes of isometry equivariant by the fundamental group of S of) mixed structures on S with a natural geometric topology, called the Gromov equivariant topology. I show, by techniques using ultralimits "à la Gromov", that the space Flat(S) of (isotopy classes of) half-translation structures on S, identified with the set of half-translation structures on the universal cover of S which are equivariant for the fundamental group of S, is a dense and open subset of Mix(S), and the projectified space PMix(S) is compact. The projectified space PMix(S) is then a compactification of the projectified space PFlat(S) (which identifies with the space of half-translations structures of area 1 on S
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Liese, Carsten [Verfasser], and Bernd [Akademischer Betreuer] Siebert. "The KSBA compactification of the moduli space of degree 2 K3 pairs : a toroidal interpretation / Carsten Liese ; Betreuer: Bernd Siebert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://d-nb.info/1164158651/34.

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Liese, Carsten Verfasser], and Bernd [Akademischer Betreuer] [Siebert. "The KSBA compactification of the moduli space of degree 2 K3 pairs : a toroidal interpretation / Carsten Liese ; Betreuer: Bernd Siebert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://nbn-resolving.de/urn:nbn:de:gbv:18-92512.

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Books on the topic "Compactification of moduli spaces"

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Hulek, Klaus. Moduli spaces of Abelian surfaces: Compactification, degenerations, and theta functions. Walter de Gruyter, 1993.

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Scattone, Francesco. On the compactification of moduli spaces for algebraic K3 surfaces. American Mathematical Society, 1987.

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Compactification of Siegel moduli schemes. Cambridge University Press, 1985.

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Brambila-Paz, Leticia, Peter Newstead, Richard P. W. Thomas, and Oscar Garcia-Prada, eds. Moduli Spaces. Cambridge University Press, 2009. http://dx.doi.org/10.1017/cbo9781107279544.

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Moduli spaces. Cambridge University Press, 2014.

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Guivarc’h, Yves, Lizhen Ji, and J. C. Taylor. Compactification of Symmetric Spaces. Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-2452-5.

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Hacking, Paul, Radu Laza, and Dragos Oprea. Compactifying Moduli Spaces. Edited by Gilberto Bini, Martí Lahoz, Emanuele Macrí, and Paolo Stellari. Springer Basel, 2016. http://dx.doi.org/10.1007/978-3-0348-0921-4.

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Kyoto, Japan) Workshop "Infinite Dimensional Teichmüller Spaces and Moduli Spaces" (2007. Infinite dimensional Teichmüller spaces and moduli spaces. Research Institute for Mathematical Sciences, Kyoto University, 2010.

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Moduli spaces of Riemann surfaces. American Mathematical Society, 2013.

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Moduli spaces and arithmetic dynamics. American Mathematical Society, 2012.

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Book chapters on the topic "Compactification of moduli spaces"

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McDuff, Dusa, and Dietmar Salamon. "Compactification of moduli spaces." In University Lecture Series. American Mathematical Society, 1994. http://dx.doi.org/10.1090/ulect/006/05.

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Donaldson, S. K. "Compactification and completion of Yang-Mills moduli spaces." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0086420.

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Laza, Radu. "Perspectives on the Construction and Compactification of Moduli Spaces." In Advanced Courses in Mathematics - CRM Barcelona. Springer Basel, 2016. http://dx.doi.org/10.1007/978-3-0348-0921-4_1.

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Martens, Johan. "Group Compactifications and Moduli Spaces." In Analytic and Algebraic Geometry. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5648-2_12.

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Louis, Jan. "Moduli Spaces of Calabi-Yau Compactifications." In M-Theory and Quantum Geometry. Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-011-4303-5_2.

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van Geemen, Bert, and Frans Oort. "A Compactification of a Fine Moduli Space of Curves." In Resolution of Singularities. Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8399-3_10.

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Kempf, George R. "Moduli Spaces." In Universitext. Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-76079-2_7.

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Cox, David, and Sheldon Katz. "Moduli spaces." In Mathematical Surveys and Monographs. American Mathematical Society, 1999. http://dx.doi.org/10.1090/surv/068/06.

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Huybrechts, Daniel, and Manfred Lehn. "Moduli Spaces." In The Geometry of Moduli Spaces of Sheaves. Vieweg+Teubner Verlag, 1997. http://dx.doi.org/10.1007/978-3-663-11624-0_4.

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Faltings, Gerd. "Moduli Spaces." In Rational Points. Vieweg+Teubner Verlag, 1986. http://dx.doi.org/10.1007/978-3-663-06812-9_1.

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Conference papers on the topic "Compactification of moduli spaces"

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Evslin, Jarah. "Noncommutativity in compactification moduli space." In STRING THEORY; 10th Tohwa University International Symposium on String Theory. AIP, 2002. http://dx.doi.org/10.1063/1.1454384.

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PENNER, R. C. "THE SIMPLICIAL COMPACTIFICATION OF RIEMANN'S MODULI SPACE." In Proceedings of the 37th Taniguchi Symposium. WORLD SCIENTIFIC, 1996. http://dx.doi.org/10.1142/9789814503921_0013.

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T. Pokorny, Florian, Kaiyu Hang, and Danica Kragic. "Grasp Moduli Spaces." In Robotics: Science and Systems 2013. Robotics: Science and Systems Foundation, 2013. http://dx.doi.org/10.15607/rss.2013.ix.036.

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Pokorny, Florian T., Yasemin Bekiroglu, and Danica Kragic. "Grasp moduli spaces and spherical harmonics." In 2014 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2014. http://dx.doi.org/10.1109/icra.2014.6906886.

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VIEHMANN, EVA. "MODULI SPACES OF LOCAL G-SHTUKAS." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0103.

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Berkenbosch, Maint. "Moduli spaces for linear differential equations." In The Conference on Differential Equations and the Stokes Phenomenon. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776549_0002.

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CAPORASO, LUCIA. "RECURSIVE COMBINATORIAL ASPECTS OF COMPACTIFIED MODULI SPACES." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0071.

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SUN, SONG. "DEGENERATIONS AND MODULI SPACES IN KÄHLER GEOMETRY." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0085.

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Fujimura, Masayo, and Kiyoko Nishizawa. "Moduli spaces and symmetry loci of polynomial maps." In the 1997 international symposium. ACM Press, 1997. http://dx.doi.org/10.1145/258726.258839.

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Cavalieri, Renzo. "Hodge-type integrals on moduli spaces of admissible covers." In The interaction of finite-type and Gromov--Witten invariants. Mathematical Sciences Publishers, 2007. http://dx.doi.org/10.2140/gtm.2006.8.167.

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Reports on the topic "Compactification of moduli spaces"

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Denef, F. Fixing All Moduli in a Simple F-Theory Compactification. Office of Scientific and Technical Information (OSTI), 2005. http://dx.doi.org/10.2172/839824.

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