Seshadri constants of equivariant vector bundles on toric varieties

TL;DR

This paper calculates Seshadri constants for equivariant nef vector bundles on toric varieties, including projective spaces and Bott towers, providing explicit values and examples under certain conditions.

Contribution

It introduces methods to compute Seshadri constants for equivariant nef vector bundles on specific toric varieties, extending understanding of their local positivity properties.

Findings

Explicit Seshadri constants for tangent bundles on projective spaces

Values of Seshadri constants on Bott towers of height 2 and 3

Examples illustrating the computation under slope conditions

Abstract

We compute Seshadri constants of a torus equivariant nef vector bundle on a projective space satisfying certain conditions. As an application, we compute Seshadri constants of tangent bundles on projective spaces. We also consider equivariant nef vector bundles on Bott towers of height 2 (i.e. Hirzebruch surfaces) and Bott towers of height 3 respectively. Assuming some conditions on the minimal slope of the restrictions of these bundles to invariant curves, we give precise values of Seshadri constant at an arbitrary point. We also give several examples illustrating our results.