An inequality for the Delta-genus of toric varieties

TL;DR

This paper establishes a lower bound for the Delta-genus of polarized toric varieties of dimension less than 5, linking it to the vanishing properties of the adjoint bundle.

Contribution

It provides a new inequality relating the Delta-genus to the vanishing number of the adjoint bundle for low-dimensional polarized toric varieties.

Findings

Delta-genus is at least n-1 for certain polarized toric varieties.

The lower bound depends on the vanishing number of the adjoint bundle.

Results are specific to varieties of dimension less than 5.

Abstract

For a polarized toric variety (X,L) of dimension n less than 5, we give a lower bound of the Delta-genus by using the vanishing number of adjoint bundle of a multiple of L. We show that for a polarized toric variety of dimension n with non-vanishing adjoint bundle, the Delta-genus is more than or equal to n-1.