Cohomology bounds for sheaves of dimension one

Abstract

We find sharp bounds on h(0)(F) for one-dimensional semistable sheaves F on a projective variety X. When X is the projective plane P-2, we study the stratification of the moduli space by the spectrum of sheaves. We show that the deepest stratum is isomorphic to a closed subset of a relative Hilbert scheme. This provides an example of a family of semistable sheaves having the biggest dimensional global section space.