Vector Bundles associated to Monads on Cartesian Products of Projective Spaces

TL;DR

This paper constructs and analyzes vector bundles derived from monads on products of projective spaces, proving their stability and simplicity, thus advancing the understanding of their geometric properties.

Contribution

It establishes the existence of specific monads on product spaces and demonstrates the stability and simplicity of the associated vector bundles, a novel contribution in this context.

Findings

Existence of monads on products of projective spaces

Stability of the constructed vector bundles

Simplicity of the vector bundles

Abstract

In this paper we construct vector bundles associated to monads on $X=\mathbb{P}^n\times\mathbb{P}^n\times\mathbb{P}^m\times\mathbb{P}^m$. We first establish the existence of such monads on $X$. Once the monads exist, the next natural question is whether the cohomology vector bundle associated to these monads are simple or not. We study these vector bundles associated to monads and prove their stability and simplicity.