A family of indecomposable rank-$n$ vector bundles on $\mathbb P^n\times\mathbb P^n$ in positive characteristics

Abstract

We construct a sequence of rank-$n$ indecomposable vector bundles on $\mathbb P^n\times\mathbb P^n$ for every $n\geq 2$ and in every positive characteristic that are not pullbacks via any map $\mathbb P^n\times\mathbb P^n\to \mathbb P^{m} $