Relevant bibliographies by topics / Curves. Geometry, Enumerative

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Curves. Geometry, Enumerative'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Curves. Geometry, Enumerative"

1

Caporaso, Lucia. "Enumerative Geometry of Plane Curves." Notices of the American Mathematical Society 67, no. 06 (2020): 1. http://dx.doi.org/10.1090/noti2094.

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Ran, Z. "Enumerative geometry of singular plane curves." Inventiones Mathematicae 97, no. 3 (1989): 447–65. http://dx.doi.org/10.1007/bf01388886.

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Do, Norman, Musashi A. Koyama, and Daniel V. Mathews. "Counting curves on surfaces." International Journal of Mathematics 28, no. 02 (2017): 1750012. http://dx.doi.org/10.1142/s0129167x17500124.

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We consider an elementary, and largely unexplored, combinatorial problem in low-dimensional topology: for a compact surface [Formula: see text], with a finite set of points [Formula: see text] fixed on its boundary, how many configurations of disjoint arcs are there on [Formula: see text] whose boundary is [Formula: see text]? We find that this enumerative problem, counting curves on surfaces, has a rich structure. We show that such curve counts obey an effective recursion, in the general spirit of topological recursion, and exhibit quasi-polynomial behavior. This “elementary curve-counting” i
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Len, Yoav, and Dhruv Ranganathan. "Enumerative geometry of elliptic curves on toric surfaces." Israel Journal of Mathematics 226, no. 1 (2018): 351–85. http://dx.doi.org/10.1007/s11856-018-1698-9.

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ALUFFI, PAOLO, and CAREL FABER. "PLANE CURVES WITH SMALL LINEAR ORBITS II." International Journal of Mathematics 11, no. 05 (2000): 591–608. http://dx.doi.org/10.1142/s0129167x00000301.

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The "linear orbit" of a plane curve of degree d is its orbit in ℙd(d+3)/2 under the natural action of PGL(3). We classify curves with positive dimensional stabilizer, and we compute the degree of the closure of the linear orbits of curves supported on unions of lines. Together with the results of [3], this encompasses the enumerative geometry of all plane curves with small linear orbit. This information will serve elsewhere as an ingredient in the computation of the degree of the orbit closure of an arbitrary plane curve.
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Yu, Tony Yue. "Gromov compactness in non-archimedean analytic geometry." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 741 (2018): 179–210. http://dx.doi.org/10.1515/crelle-2015-0077.

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Abstract Gromov’s compactness theorem for pseudo-holomorphic curves is a foundational result in symplectic geometry. It controls the compactness of the moduli space of pseudo-holomorphic curves with bounded area in a symplectic manifold. In this paper, we prove the analog of Gromov’s compactness theorem in non-archimedean analytic geometry. We work in the framework of Berkovich spaces. First, we introduce a notion of Kähler structure in non-archimedean analytic geometry using metrizations of virtual line bundles. Second, we introduce formal stacks and non-archimedean analytic stacks. Then we c
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Chiodo, Alessandro. "Towards an enumerative geometry of the moduli space of twisted curves and rth roots." Compositio Mathematica 144, no. 6 (2008): 1461–96. http://dx.doi.org/10.1112/s0010437x08003709.

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AbstractThe enumerative geometry of rth roots of line bundles is crucial in the theory of r-spin curves and occurs in the calculation of Gromov–Witten invariants of orbifolds. It requires the definition of the suitable compact moduli stack and the generalization of the standard techniques from the theory of moduli of stable curves. In a previous paper, we constructed a compact moduli stack by describing the notion of stability in the context of twisted curves. In this paper, by working with stable twisted curves, we extend Mumford’s formula for the Chern character of the Hodge bundle to the di
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KOCK, JOACHIM. "Tangency quantum cohomology and characteristic numbers." Anais da Academia Brasileira de Ciências 73, no. 3 (2001): 319–26. http://dx.doi.org/10.1590/s0001-37652001000300002.

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This work establishes a connection between gravitational quantum cohomology and enumerative geometry of rational curves (in a projective homogeneous variety) subject to conditions of infinitesimal nature like, for example, tangency. The key concept is that of modified psi classes, which are well suited for enumerative purposes and substitute the tautological psi classes of 2D gravity. The main results are two systems of differential equations for the generating function of certain top products of such classes. One is topological recursion while the other is Witten-Dijkgraaf-Verlinde-Verlinde.
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RAN, Z. "Bend, break and count II: elliptics, cuspidals, linear genera." Mathematical Proceedings of the Cambridge Philosophical Society 127, no. 1 (1999): 7–12. http://dx.doi.org/10.1017/s030500419900359x.

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In [R2] we showed how elementary considerations involving geometry on ruled surfaces may be used to obtain recursive enumerative formulae for rational plane curves. Here we show how similar considerations may be used to obtain further enumerative formulae, as follow. First some notation. As usual we denote by Ngd the number of irreducible plane curves of degree d and genus g through 3d+g−1 general points. Also, we denote by Ngd→ (resp. Ngd×) the number of such curves passing through general points A1, …, A3d+g−2 and having a given tangent direction (resp. a node) at A1. As is well known and ea
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Donovan, Will. "Contractions of 3-folds: Deformations and invariants." International Journal of Mathematics 27, no. 07 (2016): 1640004. http://dx.doi.org/10.1142/s0129167x16400048.

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This paper discusses recent new approaches to studying flopping curves on 3-folds. In a joint paper [Noncommutative deformation and flops, Duke Math. J. 165(8) (2016) 1397–1414], the author and Wemyss introduced a 3-fold invariant, the contraction algebra, which may be associated to such curves. It characterizes their geometric and homological properties in a unified manner, using the theory of noncommutative deformations. Toda has now clarified the enumerative significance of the contraction algebra for flopping curves, calculating its dimension in terms of Gopakumar-Vafa invariants [Noncommu
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Dissertations / Theses on the topic "Curves. Geometry, Enumerative"

1

Sertöz, Emre Can. "Enumerative geometry of double spin curves." Doctoral thesis, Humboldt-Universität zu Berlin, 2017. http://dx.doi.org/10.18452/18455.

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Diese Dissertation hat zwei Teile. Im ersten Teil untersuchen wir die Modulräume von Kurven mit multiplen Spinstrukturen. Wir stellen eine neue Kompaktifizierung dieser Räume mit geometrisch sinnvollem Grenzverhalten vor. Die irreduziblen Komponenten dieser Räume werden vollstandig klassifiziert. Die Ergebnisse aus diesem ersten Teil der Dissertation sind fundamental für die Degenerationstechniken im zweiten Teil. Im zweiten Teil untersuchen wir eine Reihe von Problemen, die von der klassischen Geometrie inspiriert werden. Unser Hauptaugenmerk liegt hierbei auf dem Fall von zwei Hypereben
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Van, Zelm J. "The enumerative geometry of double covers of curves." Thesis, University of Liverpool, 2018. http://livrepository.liverpool.ac.uk/3022475/.

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Let Adm(g, h)_2m be the space of admissible double covers C → D of curves of genus g and h, with all the ramification and branch points of C and D marked, and where the covering involution permutes an extra set of 2m marked points of C pairwise. For each 0 ≤ n ≤ 2g +2−4h there is a natural map φ_n : Adm(g, h)_2m → Mbar_g,n+2m mapping the admissible cover C → D to the stabilization of the source curve C together with the 2m points and the first n ramification points. In this thesis we will study classes of the form [φ_n (Adm(g, h)_2m )] in the Chow ring of Mbar_g,n+2m . We will derive a formula
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Ungureanu, Mara. "Enumerative formulas of de Jonquières type on algebraic curves." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/19660.

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Diese Arbeit widmet sich der Untersuchung von zwei Problemen der abzählenden Geometrie im Zusammenhang mit linearen Systemen auf algebraischen Kurven. Das erste Problem besteht darin, die Frage der Gültigkeit der Jonquières-Formeln zu klären. Diese Formeln berechnen die Anzahl von Divisoren mit vorgeschriebener Multiplizität, genannt de Jonquières-Divisoren, die in einem linearen System auf einer glatten projektiven Kurve enthalten sind. Um dies zu tun, konstruieren wir den Raum der de Jonquières-Divisoren als einen Determinantenzyklus des symmetrischen Produkts der Kurve und beweisen, dass
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Torchiani, Carolin [Verfasser]. "Enumerative geometry of rational and elliptic tropical curves in R m / Carolin Torchiani." München : Verlag Dr. Hut, 2014. http://d-nb.info/1055863834/34.

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Sertöz, Emre Can [Verfasser], Gavril [Gutachter] Farkas, and Samuel [Gutachter] Grushevsky. "Enumerative geometry of double spin curves / Emre Can Sertöz ; Gutachter: Gavril Farkas, Samuel Grushevsky." Berlin : Humboldt-Universität zu Berlin, 2017. http://d-nb.info/119869226X/34.

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Blomme, Thomas. "Computation of Refined Enumerative Invariants in Real and Tropical Geometry." Thesis, Sorbonne université, 2020. http://www.theses.fr/2020SORUS016.

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La géométrie tropicale a permis le calcul de nombreux invariants de géométrie complexe (invariants de Gromov-Witten), ainsi que réelle (invariants de Welschinger) à travers l'utilisation de théorèmes de correspondance. Ceux-ci mettent à jour des liens profonds entre la géométrie tropicale et la géométrie dite classique. La richesse des objets tropicaux alliée à leur simplicité apparente a également permis de proposer de nouveaux invariants, dits raffinés, dont les interprétations en géométrie classique restent à ce jour encore mystérieuses, bien que plusieurs conjectures, comme celle de Göttsc
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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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Santos, Renan da Silva. "Geometria enumerativa via invariantes de Gromov-Witten e mapas estÃveis." Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=14326.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior<br>Neste trabalho apresento a teoria de Gromov-Witten, cohomologia quÃntica e mapas estÃveis e uso estas ferramentas para obter alguns resultados enumerativos. Em particular, provo a fÃrmula de Kontsevich para curvas racionais projetivas planas de grau d. FaÃo um estudo introdutÃrio dos espaÃos de Mumford-Knudsen e construo os espaÃos de Kontsevich a fim de definir os invariantes de Gromov-Witten. Estes sÃo usados para definir o anel de cohomologia quÃntica. Em seguida, aplico a teoria geral para o caso do plano projetivo e, usando a a
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Santos, Renan da Silva. "Geometria enumerativa via invariantes de Gromov-Witten e mapas estáveis." reponame:Repositório Institucional da UFC, 2015. http://www.repositorio.ufc.br/handle/riufc/12544.

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SANTOS, Renan da Silva. Geometria enumerativa via invariantes de Gromov-Witten e mapas estáveis. 2015. 78 f. Dissertação (mestrado) - Universidade Federal do Ceará, Centro de Ciências, Programa de Pós-Graduação em Matemática, Fortaleza-Ce, 2015<br>Submitted by Erivan Almeida (eneiro@bol.com.br) on 2015-05-29T18:19:53Z No. of bitstreams: 1 2015_dis_rssantos.pdf: 870583 bytes, checksum: f5ebc0c90f1e8aaca61f2be5057d0448 (MD5)<br>Approved for entry into archive by Rocilda Sales(rocilda@ufc.br) on 2015-06-01T10:53:48Z (GMT) No. of bitstreams: 1 2015_dis_rssantos.pdf: 870583 bytes, checksum: f5ebc0c
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Lima, Fábio Pereira. "Deformação e alguns números característicos de certas famílias de curvas." Universidade Federal de Pernambuco, 2012. https://repositorio.ufpe.br/handle/123456789/11683.

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Submitted by Etelvina Domingos (etelvina.domingos@ufpe.br) on 2015-03-10T16:45:51Z No. of bitstreams: 2 fabio_pereira_lima.pdf: 3336336 bytes, checksum: c5b05c14e17b2bf72e2cfc7d668894b7 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5)<br>Made available in DSpace on 2015-03-10T16:45:51Z (GMT). No. of bitstreams: 2 fabio_pereira_lima.pdf: 3336336 bytes, checksum: c5b05c14e17b2bf72e2cfc7d668894b7 (MD5) license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Previous issue date: 2012<br>CNPq<br>Nesta dissertação, faremos uma construção geométrica
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Books on the topic "Curves. Geometry, Enumerative"

1

(Dietmar), Salamon D., ed. J-holomorphic curves and symplectic topology. 2nd ed. American Mathematical Society, 2012.

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2

An Invitation to Quantum Cohomology: Kontsevich's Formula for Rational Plane Curves (Progress in Mathematics). Birkhäuser Boston, 2006.

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3

Kock, Joachim, and Israel Vainsencher. An Invitation to Quantum Cohomology. Springer, 2008.

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A Celebration of Algebraic Geometry (Clay Mathematics Proceedings). American Mathematical Society, 2013.

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Athorne, Chris, 1957- editor of compilation, Maclagan, Diane, 1974- editor of compilation, and Strachan, Ian, 1965- editor of compilation, eds. Tropical geometry and integrable systems: Conference on Tropical Geometry and Integrable Systems, July 3-8, 2011, University of Glasgow, Glasgow, United Kingdom. 2012.

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Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices Ams Special Session Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices January 67 2012 Boston Ma. American Mathematical Society, 2013.

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Book chapters on the topic "Curves. Geometry, Enumerative"

1

Arbarello, E., M. Cornalba, P. A. Griffiths, and J. Harris. "Enumerative Geometry of Curves." In Grundlehren der mathematischen Wissenschaften. Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4757-5323-3_8.

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Katz, Sheldon. "Rational curves on the quintic threefold." In Enumerative Geometry and String Theory. American Mathematical Society, 2006. http://dx.doi.org/10.1090/stml/032/09.

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Mumford, David. "Towards an Enumerative Geometry of the Moduli Space of Curves." In Selected Papers. Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4757-4265-7_9.

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"A note on enumerating rational curves in a K3 surface." In Geometry and Nonlinear Partial Differential Equations. American Mathematical Society, 2002. http://dx.doi.org/10.1090/amsip/029/07.

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You might also be interested in the extended bibliographies on the topic 'Curves. Geometry, Enumerative' for particular source types:
Journal articles
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