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

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

2006-09-29

arxiv.org/abs/math/0610004v4

Mathematics

Symplectic Geometry

Final version. 75 pages, 12 figures

Scientific paper

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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