Moduli of Stable Sheaves on a Smooth Quadric in $\PP_3$

TL;DR

This paper establishes an isomorphism between the moduli space of certain stable sheaves on a smooth quadric in projective 3-space and projective 3-space itself, providing new insights into related Brill-Noether loci.

Contribution

It proves the isomorphism of the moduli space of rank 2 stable sheaves with specific Chern classes on a smooth quadric in P3 to P3, and offers a new proof of a related Brill-Noether locus identification.

Findings

Moduli space of stable sheaves is isomorphic to P3.

New proof of Brill-Noether locus isomorphism to Donagi-Izadi cubic threefold.

Clarifies geometric structure of sheaves on quadrics.

Abstract

We prove that the moduli space of stable sheaves of rank 2 with a certain Chern classes on a smooth quadric $Q$ in $\PP_3$, is isomorphic to $\PP_3$. Using this identification, we give a new proof that a certain Brill-Noether locus on a non-hyperelliptic curve of genus 4, is isomorphic to the Donagi-Izadi cubic threefold.