Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for P1 a,b,c

Cheol Hyun Cho, Hansol Hong, Siu Cheong Lau

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper gives a new way of constructing Landau-Ginzburg mirrors using deformation theory of Lagrangian immersions motivated by the works of Seidel, Strominger-Yau-Zaslow and Fukaya- Oh-Ohta-Ono. Moreover, we construct a canonical functor from the Fukaya category to the mirror category of matrix factorizations. This functor derives homological mirror symmetry under some explicit assumptions. As an application, the construction is applied to spheres with three orbifold points to produce their quantum-corrected mirrors and derive homological mirror symmetry. Furthermore, we discover an enumerative meaning of the (inverse) mirror map for elliptic curve quotients.

Original languageEnglish
Pages (from-to)45-126
Number of pages82
JournalJournal of Differential Geometry
Volume106
Issue number1
DOIs
Publication statusPublished - 2017 Apr

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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