Vector bundles associated to monads on cartesian products of projective spaces

Abstract

In this paper we establish the existence of monads on cartesian products of projective spaces. We give the necessary and sufficient conditions for the existence of monads on \(\mathbf{P}^1\times\cdots\times \mathbf{P}^1\). We construct vector bundles associated to monads on \(X=\mathbf{P}^n\times\mathbf{P}^n\times\mathbf{P}^m\times\mathbf{P}^m\). We study these vector bundles associated to monads on \(X\) and prove their stability and simplicity.