On two moduli spaces of sheaves supported on quadric surfaces

TL;DR

This paper characterizes a specific moduli space of semi-stable sheaves on a smooth quadric surface, revealing it as a blow-up of a hypersurface in a weighted projective space, thus providing geometric insights into its structure.

Contribution

It identifies the geometric structure of a particular moduli space of sheaves on a quadric surface as a blow-up of a hypersurface in weighted projective space.

Findings

The moduli space is the blow-up at two points of a hypersurface.

Provides explicit geometric description of the moduli space.

Connects sheaf moduli to weighted projective space geometry.

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.