Volume 10, issue 2 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Homogeneous coordinate rings and mirror symmetry for toric varieties

Mohammed Abouzaid

Geometry & Topology 10 (2006) 1097–1156

arXiv: math.SG/0511644

Abstract

Given a smooth toric variety X and an ample line bundle O(1), we construct a sequence of Lagrangian submanifolds of ()n with boundary on a level set of the Landau–Ginzburg mirror of X. The corresponding Floer homology groups form a graded algebra under the cup product which is canonically isomorphic to the homogeneous coordinate ring of X.

Keywords
homological mirror symmetry, toric varieties, tropical geometry
Mathematical Subject Classification 2000
Primary: 14J32
Secondary: 53D40
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Publication
Received: 26 November 2005
Revised: 3 May 2006
Accepted: 1 June 2006
Published: 24 August 2006
Proposed: Jim Bryan
Seconded: Lothar Göttsche, Simon Donaldson
Authors
Mohammed Abouzaid
Department of Mathematics
University of Chicago
Chicago, IL 60637
USA