On two moduli spaces of sheaves supported on quadric surfaces

Abstract

We show that the moduli space of semi-stable sheaves on a smooth quadric surface, having dimension 1, multiplicity 4, Euler characteristic 2, and first Chern class (2, 2), is the blow-up at two points of a certain hypersurface in a weighted projective space.

arXiv commentSecond version contains a more general rationality result (Prop. 3)