Irreducibility of the moduli space of stable vector bundles of rank two and odd degree on a very general quintic surface

TL;DR

This paper proves that the moduli space of stable rank two vector bundles with odd degree on a very general quintic surface is irreducible for all second Chern classes greater than or equal to four, and empty otherwise.

Contribution

It establishes the irreducibility and emptiness of the moduli space of stable rank two vector bundles on a very general quintic surface depending on the second Chern class.

Findings

Moduli space is irreducible for all c_2 ≥ 4.

Moduli space is empty for c_2 < 4.

Results apply to very general quintic surfaces.

Abstract

The moduli space $M(c_2)$, of stable rank two vector bundles of degree one on a very general quintic surface $X\subset {\mathbb P}^3$, is irreducible for all $c_2\geq 4$ and empty otherwise.