Title:

Tropical Calabi-Yau Mirrors in non-Fano Toric Varieties

We consider non-convex Newton polyhedra to describe non-Fano toric varieties. Taking a general anticanonical section, we obtain a Calabi-Yau hypersurface on which we consider a nonlinear sigma model realized as a geometric phase of a GLSM. We study mirror symmetry of such Calabi-Yau manifolds via an extension of Batryev’s construction based on the duality of reflexive polytopes. Using the mirror pair from this construction we show that, in a tropical limit, the Gamma-conjecture still holds for some examples of Calabi-Yau hypersurfaces in these generalized ambient spaces. With a period formula that I derived, we are now working to extend our results to a homological mirror symmetry statement.

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