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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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Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves
Інший ID:
2010 Mathematics Subject Classification: 53D37; 14J33; 14J32; 14J45; 14D06
DOI:10.3842/SIGMA.2017.024
DOI:10.3842/SIGMA.2017.024
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
498
Завантажень:
275
Анотація:
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.
