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

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts 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 $\mathsc{O}\left(1\right)$, 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