A Few Splitting Criteria for Vector Bundles

TL;DR

This paper establishes new splitting criteria for vector bundles on quadrics, Grassmannians, and multiprojective spaces using monads and spectral sequences, advancing the understanding of vector bundle decompositions.

Contribution

It introduces novel cohomological splitting conditions and criteria for vector bundles on various algebraic varieties, utilizing advanced spectral sequence techniques.

Findings

New splitting criteria for vector bundles on quadrics and Grassmannians

Cohomological conditions for rank 2 bundles on multiprojective spaces

Application of generalized Beilinson spectral sequences

Abstract

We prove a few splitting criteria for vector bundles on a quadric hypersurface and Grassmannians. We give also some cohomological splitting conditions for rank 2 bundles on multiprojective spaces. The tools are monads and a Beilinson's type spectral sequence generalized by Costa and Mir\'o-Roig.