@article{07a41827326c435fb31825b3087b70c6,

title = "Doran–Harder–Thompson conjecture via SYZ mirror symmetry: Elliptic curves",

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 = "Affine geometry, Calabi–Yau manifolds, Fano manifolds, Landau–Ginzburg models, SYZ mirror symmetry, Tyurin degeneration",

author = "Atsushi Kanazawa",

note = "Funding Information: 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{\textquoteright}s stay at BIRS in the fall of 2016. Publisher Copyright: {\textcopyright} 2017, Institute of Mathematics. All rights reserved.",

year = "2017",

month = apr,

day = "11",

doi = "10.3842/SIGMA.2017.024",

language = "English",

volume = "13",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

issn = "1815-0659",

publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}