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

TL;DR

This paper extends the understanding of Calabi-Yau hypersurfaces in non-Fano toric varieties by analyzing their periods and confirming the $\

Contribution

It introduces a multi-polytope framework for non-Fano toric varieties and verifies the $\

Findings

The $\

The $\

The $\

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 $\widehat{\Gamma}$-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.