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

Mohammed Abouzaid
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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.

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Mohammed Abouzaid. 2009-04-21. Morse Homology, Tropical Geometry, and Homological Mirror Symmetry for Toric Varieties. https://arxiv.org/abs/math/0610004

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