Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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dc.contributor.author	Kanazawa, A.
dc.date.accessioned	2019-02-18T16:29:46Z
dc.date.available	2019-02-18T16:29:46Z
dc.date.issued	2017
dc.identifier.citation	Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves / A. Kanazawa // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 21 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 53D37; 14J33; 14J32; 14J45; 14D06
dc.identifier.other	DOI:10.3842/SIGMA.2017.024
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148604
dc.description.abstract	We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi-Yau manifold X degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi-Yau manifold of X can be constructed by gluing the two mirror Landau-Ginzburg models of the quasi-Fano manifolds. The two crucial ideas in our proof are to obtain a complex structure by gluing the underlying affine manifolds and to construct the theta functions from the Landau-Ginzburg superpotentials.	uk_UA
dc.description.sponsorship	The author would like to thank Yu-Wei Fan, Andrew Harder, Hansol Hong and Siu-Cheong Lau for useful conversations on related topics. Special thanks go to the referees for their valuable comments and improvements to this article. This research was supported by the Kyoto University Hakubi Project. Part of this work was carried out during the author’s stay at BIRS in the fall of 2016.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA