The Kodaira-Spencer map for minimal toric hypersurfaces

TL;DR

This paper investigates infinitesimal deformations of toric hypersurfaces, introduces a Kodaira-Spencer map, and computes its kernel explicitly, generalizing classical results for projective hypersurfaces.

Contribution

It provides an explicit computation of the Kodaira-Spencer map for toric hypersurfaces, extending Griffiths' work to a broader class of varieties.

Findings

Explicit formula for the Kodaira-Spencer map kernel

Generalization of Griffiths' results to toric hypersurfaces

Introduction of new Laurent polynomials for computations

Abstract

In this article we study infinitesimal deformations of toric hypersurfaces. We introduce a Kodaira-Spencer map and compute its kernel. By introducing some new Laurent polynomials we make our computation as explicit as possible. This widely generalizes results of Griffiths for projective hypersurfaces.