Simple Cohomology bundles on multiprojective spaces

TL;DR

This paper investigates the stability and simplicity of cohomology bundles on multiprojective spaces, specifically for vector bundles associated with monads on products of projective spaces, under certain ample line bundles.

Contribution

It establishes the stability of the kernel bundle and the simplicity of the cohomology bundle for a class of vector bundles on multiprojective spaces, extending understanding of their geometric properties.

Findings

Kernel bundle is stable.

Cohomology bundle is simple.

Results apply to bundles associated with monads on multiprojective spaces.

Abstract

We prove stability of the kernel bundle and prove that the cohomology bundle is simple for vector bundles associated to monads on $X = (\mathbb{P}^{n_1})^2\times\cdots\times(\mathbb{P}^{n_s})^2$ for an ample line bundle $\mathscr{L}=\mathcal{O}_X(\alpha_1,\alpha_1,\cdots,\alpha_s,\alpha_s)$.