Differential forms and Hodge numbers for toric complete intersections

TL;DR

This paper develops methods to compute Hodge numbers of quasi-smooth complete intersections in toric varieties by analyzing differential forms and Euler characteristics, extending previous approaches to symmetric and arbitrary forms.

Contribution

It introduces conditions for calculating Hodge numbers in toric complete intersections and generalizes the computation of Euler characteristics for various differential forms.

Findings

Derived conditions for computing Hodge numbers in toric varieties.

Extended Euler characteristic calculations to symmetric and arbitrary differential forms.

Provided a framework for analyzing quasi-smooth complete intersections.

Abstract

We discuss conditions for complete intersections in a toric variety which allow to compute Hodge numbers if the complete intersection is a quasi-smooth complete variety. A preliminary step is the computation of the Euler characteristic of differential forms, we also look at symmetric or arbitrary forms instead of the usual alternating ones.