Simple Cohomology bundles on multiprojective spaces

Abstract

We prove stability of the kernel bundle and prove that the cohomology bundle is simple for vector bundles associated to monads on $X = (\mathbb{P}^{n_1})^2\times\cdots\times(\mathbb{P}^{n_s})^2$ for an ample line bundle $\mathscr{L}=\mathcal{O}_X(\alpha_1,\alpha_1,\cdots,\alpha_s,\alpha_s)$.