Local Calabi–Yau manifolds of type A˜ via SYZ mirror symmetry

Atsushi Kanazawa, Siu Cheong Lau

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


We carry out the SYZ program for the local Calabi–Yau manifolds of type A˜ by developing an equivariant SYZ theory for the toric Calabi–Yau manifolds of infinite-type. Mirror geometry is shown to be expressed in terms of the Riemann theta functions and generating functions of open Gromov–Witten invariants, whose modular properties are found and studied in this article. Our work also provides a mathematical justification for a mirror symmetry assertion of the physicists Hollowood–Iqbal–Vafa (Hollowood et al., 2008).

Original languageEnglish
Pages (from-to)103-138
Number of pages36
JournalJournal of Geometry and Physics
Publication statusPublished - 2019 May
Externally publishedYes


  • Abelian varieties
  • Calabi–Yau manifolds
  • Riemann theta functions
  • SYZ mirror symmetry
  • Toric geometry
  • open Gromov–Witten invariants

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology


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