Morse Homology, Tropical Geometry, and Homological Mirror Symmetry for Toric Varieties

Abstract

Given a smooth projective toric variety X, we construct an A-infinity category of Lagrangians with boundary on a level set of the Landau-Ginzburg mirror of X. We prove that this category is quasi-equivalent to the DG category of line bundles on X. This establishes part of the Homological Mirror Conjecture for toric varieties.

Final version. 75 pages, 12 figures

References in corpus (1)

• The Morse Complex for a Morse Function on a Manifold with Corners

Cited by in corpus (1)

• On the conjecture of King for smooth toric Deligne-Mumford stacks