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This article is cited in 2 scientific papers (total in 2 papers)
Doran–Harder–Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves
Atsushi Kanazawa Department of Mathematics, Kyoto University, Kitashirakawa-Oiwake, Sakyo, Kyoto, 606-8502, Japan
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.
Keywords:
Calabi–Yau manifolds; Fano manifolds; SYZ mirror symmetry; Landau–Ginzburg models; Tyurin degeneration; affine geometry.
Received: December 20, 2016; in final form April 6, 2017; Published online April 11, 2017
Citation:
Atsushi Kanazawa, “Doran–Harder–Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves”, SIGMA, 13 (2017), 024, 13 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1224 https://www.mathnet.ru/eng/sigma/v13/p24
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