Indecomposable vector bundles via monads on P2n+1 × P2n+1

Abstract

The existence of monads on products of projective spaces $P^{a_1}\times\cdots\times\ P^{a_n}$ is nontrivial. In this paper, we construct monads over the polycyclic variety $P^{2n+1}\times\ P^{2n+1}$, we prove that cohomology vector bundle associated to these monads is simple. We also construct a monad on $P^1\times P^1\times\ P^2$. We also study the vector bundles associated to monads and prove stability and simplicity.