Splitting of Vector Bundles on Toric Varieties

TL;DR

This paper establishes a new criterion for decomposing vector bundles into simpler components on smooth projective toric varieties, extending classical results to a broader class of algebraic varieties.

Contribution

It introduces a Horrocks-type splitting criterion applicable to all smooth projective toric varieties under specific conditions, generalizing previous special cases.

Findings

Proves a splitting criterion for vector bundles on toric varieties.

Extends classical splitting results to a wider class of algebraic varieties.

Provides conditions under which vector bundles decompose into simpler parts.

Abstract

We prove a Horrocks-type splitting criterion for arbitrary smooth projective toric varieties under an additional hypothesis similar to the case of products of projective spaces by Eisenbud--Erman--Schreyer.