Regularity and Cohomological Splitting Conditions for Vector Bundles on Multiprojective Spaces

TL;DR

This paper introduces a new notion of regularity for vector bundles on multiprojective spaces and establishes splitting criteria based on this concept, differing from previous definitions.

Contribution

It proposes a novel regularity definition on multiprojective spaces and derives new splitting conditions for vector bundles using this framework.

Findings

New regularity notion for multiprojective spaces

Splitting criteria for vector bundles established

Different from Hoffmann-Wang and Costa-Miró Roig definitions

Abstract

Here we give a definition of regularity on multiprojective spaces which is different from the definitions of Hoffmann-Wang and Costa-Mir\'o Roig. By using this notion we prove some splitting criteria for vector bundles.