A Horrocks' theorem for reflexive sheaves

Abstract

In this paper, we define $m$-tail reflexive sheaves as reflexive sheaves on projective spaces with the simplest possible cohomology. We prove that the rank of any $m$-tail reflexive sheaf $\mathcal{E}$ on ${\mathcal{P}}^n$ is greater or equal to $nm-m$. We completely describe $m$-tail reflexive sheaves on ${\mathcal{P}}^n$ of minimal rank and we construct huge families of $m$-tail reflexive sheaves of higher rank.

to appear in Journal of Algebra