Homogeneous coordinate rings and mirror symmetry for toric varieties

Abouzaid, Mohammed¹

¹ Department of Mathematics, University of Chicago, Chicago, IL 60637, USA

Geometry & topology, Tome 10 (2006) no. 2, pp. 1097-1156.

Résumé

Given a smooth toric variety $X$ and an ample line bundle $\mathcal{O}\left(1\right)$, 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 $X$.

Détail

DOI : 10.2140/gt.2006.10.1097

Keywords: homological mirror symmetry, toric varieties, tropical geometry

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