M. Abouzaid, D. Auroux, A. I. Efimov, L. Katzarkov, D. Orlov, “Homological mirror symmetry for punctured spheres”, Journal of the American Mathematical Society, 2013, том 26, выпуск 4, страницы 1051

Journal of the American Mathematical Society

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ЖУРНАЛЫ ПЕРСОНАЛИИ ОРГАНИЗАЦИИ КОНФЕРЕНЦИИ СЕМИНАРЫ ВИДЕОТЕКА ПАКЕТ AMSBIB

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Journal of the American Mathematical Society, 2013, том 26, выпуск 4, страницы 1051–1083
DOI: https://doi.org/10.1090/S0894-0347-2013-00770-5 (Mi jams2)

Эта публикация цитируется в 29 научных статьях (всего в 29 статьях)

Homological mirror symmetry for punctured spheres

M. Abouzaid^a, D. Auroux^b, A. I. Efimov^c, L. Katzarkov^de, D. Orlov^c

^a Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
^b Department of Mathematics, University of California, Berkeley, Berkeley, California 94720-3840
^c Algebraic Geometry Section, Steklov Mathematical Institute, Russian Academy of Sciences, 8 Gubkin Street, Moscow 119991, Russia
^d Department of Mathematics, Universität Wien, Garnisongasse 3, Vienna A-1090, Austria
^e University of Miami, P.O. Box 249085, Coral Gables, Florida 33124-4250

Список цитирования (29)

DOI: https://doi.org/10.1090/S0894-0347-2013-00770-5

Аннотация: We prove that the wrapped Fukaya category of a punctured sphere ($ S^{2}$ with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror Landau-Ginzburg model, proving one side of the homological mirror symmetry conjecture in this case. By investigating fractional gradings on these categories, we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the Landau–Ginzburg model.

Финансовая поддержка	Номер гранта
National Science Foundation	DMS-0652630 DMS-1007177 DMS-0600800 DMS-0652633
Фонд Дмитрия Зимина «Династия»	4713.2010.1
Министерство образования и науки Российской Федерации	11.G34.31.0023
Austrian Science Fund	P20778
European Research Council	GEMIS
Российский фонд фундаментальных исследований	10-01-93113 11-01-00336 11-01-00568
The first author was supported by a Clay Research Fellowship. The second author was partially supported by NSF grants DMS-0652630 and DMS-1007177. The third author was partially supported by the Dynasty Foundation, NSh grant 4713.2010.1, and by AG Laboratory HSE, RF government grant, ag. 11.G34.31.0023. The fourth author was funded by NSF grant DMS-0600800, NSF FRG grant DMS-0652633, FWF grant P20778, and an ERC grant – GEMIS. The last author was partially supported by RFBR grants 10-01-93113, 11-01-00336, 11-01-00568, NSh grant 4713.2010.1, and by AG Laboratory HSE, RF government grant, ag. 11.G34.31.0023.

Поступила в редакцию: 22.03.2011
Исправленный вариант: 02.03.2013

Реферативные базы данных:

Тип публикации: Статья

MSC: Primary 53D37, 14J33; Secondary 53D40, 53D12, 18E30, 14F05

Язык публикации: английский

Образцы ссылок на эту страницу:

https://www.mathnet.ru/rus/jams2

Эта публикация цитируется в следующих 29 статьяx:

Raf Bocklandt, Jasper van de Kreeke, Contemporary Mathematics, 801, Recent Advances in Noncommutative Algebra and Geometry, 2024, 17
Valentin Bosshard, “Lagrangian cobordisms in Liouville manifolds”, J. Topol. Anal., 16:05 (2024), 777
Denis Auroux, Alexander I. Efimov, Ludmil Katzarkov, “Lagrangian Floer theory for trivalent graphs and homological mirror symmetry for curves”, Sel. Math. New Ser., 30:5 (2024)
Mohammed Abouzaid, Denis Auroux, “Homological mirror symmetry for hypersurfaces in (ℂ∗)n”, Geom. Topol., 28:6 (2024), 2825
Christopher Kuo, “Wrapped sheaves”, Advances in Mathematics, 415 (2023), 108882
Denis Auroux, Ivan Smith, “Fukaya categories of surfaces, spherical objects and mapping class groups”, Forum of Mathematics, Sigma, 9 (2021)
Michael Wong, “Dimer models and Hochschild cohomology”, Journal of Algebra, 585 (2021), 207
Fabian Haiden, “Legendrian skein algebras and Hall algebras”, Math. Ann., 381:1-2 (2021), 631
Haniya Azam, Catherine Cannizzo, Heather Lee, Association for Women in Mathematics Series, 27, Research Directions in Symplectic and Contact Geometry and Topology, 2021, 159
Claudius Zibrowius, “Peculiar modules for 4‐ended tangles”, Journal of Topology, 13:1 (2020), 77
James Pascaleff, Nicolò Sibilla, “Topological Fukaya category and mirror symmetry for punctured surfaces”, Compositio Math., 155:3 (2019), 599
Benjamin Gammage, David Nadler, “Mirror symmetry for honeycombs”, Trans. Amer. Math. Soc., 373:1 (2019), 71
David Nadler, “Mirror symmetry for the Landau–Ginzburg A-model M=Cn, W=z1⋯zn”, Duke Math. J., 168:1 (2019)
Ailsa Keating, “Homological mirror symmetry for hypersurface cusp singularities”, Sel. Math. New Ser., 24:2 (2018), 1411
Yankı Lekili, Alexander Polishchuk, “Auslander orders over nodal stacky curves and partially wrapped Fukaya categories”, Journal of Topology, 11:3 (2018), 615
Mark Gross, Ludmil Katzarkov, Helge Ruddat, “Towards mirror symmetry for varieties of general type”, Advances in Mathematics, 308 (2017), 208
David Nadler, “A combinatorial calculation of the Landau–Ginzburg model $M={\mathbb {C}}^{3},W=z_1 z_2 z_3$ M = C 3 , W = z 1 z 2 z 3”, Sel. Math. New Ser., 23:1 (2017), 519
Alexander F. Ritter, Ivan Smith, “The monotone wrapped Fukaya category and the open-closed string map”, Sel. Math. New Ser., 23:1 (2017), 533
Andrew Harder, Ludmil Katzarkov, Yijia Liu, Simons Symposia, Geometry Over Nonclosed Fields, 2017, 53
Gabriel Kerr, “Homological mirror symmetry of elementary birational cobordisms”, Sel. Math. New Ser., 23:4 (2017), 2801

Citing articles in Google Scholar: Russian citations, English citations
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