Homogeneous coordinate rings and mirror symmetry for toric varieties

Mathematics – Symplectic Geometry

Scientific paper

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This is the version published by Geometry & Topology on 24 August 2006

Scientific paper

10.2140/gt.2006.10.1097

Given a smooth toric variety X and an ample line bundle O(1), we construct a
sequence of Lagrangian submanifolds of (C^*)^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.

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