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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Author: Kanazawa, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148604
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...