Cohomology bounds for sheaves of dimension one

Abstract

We find the sharp bounds on $h^0(F)$ for one-dimensional semistable sheaves $F$ on a projective variety $X$ by using the spectrum of semistable sheaves. The result generalizes the Clifford theorem. When $X$ is the projective plane ${\mathbb{P}}^2$, we study the stratification of the moduli space by the spectrum of sheaves. We show that the deepest stratum is isomorphic to a subscheme of a relative Hilbert scheme. This provides an example of a family of semistable sheaves having the biggest dimensional global section space.

17 pages, no figures. Comments are welcome. The result has been generalized to a projective variety

References in corpus (1)

• On the geometry of the moduli spaces of semistable sheaves supported on plane quartics

Cited by in corpus (3)

• The geometry of the moduli space of one-dimensional sheaves
• Virtual Poincaré polynomial of the space of stable pairs supported on quintic curves
• Moduli of sheaves, Fourier-Mukai transform, and partial desingularization