Selecta Mathematica

, Volume 15, Issue 2, pp 189–270

Morse homology, tropical geometry, and homological mirror symmetry for toric varieties

Article

DOI: 10.1007/s00029-009-0492-2

Cite this article as:
Abouzaid, M. Sel. Math. New Ser. (2009) 15: 189. doi:10.1007/s00029-009-0492-2

Abstract.

Given a smooth projective toric variety X, we construct an A 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.

Mathematics Subject Classification (2000).

14J32 53D40 58E05 

Keywords.

Homological mirror symmetry toric varieties tropical geometry Lagrangian Floer homology Morse homology 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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