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. 1.
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Mohammed Abouzaid (2006) studied this question.