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

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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.

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  1. Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA, 02139-4307, USA

    Mohammed Abouzaid

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  1. Mohammed Abouzaid
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Correspondence to Mohammed Abouzaid.

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Abouzaid, M. Morse homology, tropical geometry, and homological mirror symmetry for toric varieties. Sel. Math. New Ser. 15, 189–270 (2009). https://doi.org/10.1007/s00029-009-0492-2

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  • DOI: https://doi.org/10.1007/s00029-009-0492-2

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