#### Volume 10, issue 2 (2006)

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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 $\mathsc{O}\left(1\right)$, we construct a sequence of Lagrangian submanifolds of ${\left({ℂ}^{\star }\right)}^{n}$ 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
Primary: 14J32
Secondary: 53D40
##### 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