The Coherent-Constructible Correspondence and Homological Mirror Symmetry for Toric Varieties
Bohan Fang, Chiu-Chu Melissa Liu, David Treumann, Eric Zaslow
TL;DR
This paper explains recent advances connecting microlocalization, Fukaya categories, and coherent sheaves on toric varieties, highlighting their role in homological mirror symmetry.
Contribution
It provides an exposition of new results linking microlocal sheaf theory and symplectic geometry in the context of toric varieties.
Findings
Establishment of the coherent-constructible correspondence for toric varieties
Connections between microlocal sheaves and Fukaya categories
Progress towards homological mirror symmetry for toric varieties
Abstract
This is an expository article describing recent results of the authors and David Nadler on microlocalization, the Fukaya category, and coherent sheaves on toric varieties. The original papers are arXiv:math/0604379, arXiv:math/0612399 and arXiv:0811.1228v1.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry