Doran–Harder–Thompson conjecture via SYZ mirror symmetry: Elliptic curves

Atsushi Kanazawa

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Article number024
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume13
DOIs
Publication statusPublished - 2017 Apr 11
Externally publishedYes

Keywords

  • Affine geometry
  • Calabi–Yau manifolds
  • Fano manifolds
  • Landau–Ginzburg models
  • SYZ mirror symmetry
  • Tyurin degeneration

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

Fingerprint

Dive into the research topics of 'Doran–Harder–Thompson conjecture via SYZ mirror symmetry: Elliptic curves'. Together they form a unique fingerprint.

Cite this