Tropical Periods for Calabi-Yau Hypersurfaces in non--Fano Toric Varieties

Abstract

We consider multi-polytopes to describe non-Fano toric varieties and their associated anticanonical Calabi-Yau hypersurfaces. From the periods of the mirror manifold the $\hat{\Gamma }$-conjecture is shown to hold for examples of Calabi-Yau hypersurfaces in non-Fano ambient spaces, extending earlier work by Abouzaid et al by employing a generalized Duistermaat-Heckman measure.

arXiv comment43 pages, 6 figures. References added and minor edits to section 1