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

Abstract

The existence of monads on products of projective spaces P a1 × · · · × P an is nontrivial. In this paper, we construct monads over the polycyclic variety P 2n+1 × P 2n+1 , we prove that cohomology vector bundle associated to these monads is simple. We also construct a monad on P 1 × P 1 × P 2 . We also study the vector bundles associated to monads and prove stability and simplicity.