The irreducibility of the moduli space of stable vector bundles of rank 2 on a quintic in $\pp^3$

TL;DR

This paper proves that the moduli space of rank 2 stable vector bundles with fixed Chern classes on a general quintic surface in projective 3-space is irreducible for second Chern class c2 at least 16, extending previous results.

Contribution

It establishes an explicit bound c2 ≥ 16 for the irreducibility of the moduli space of stable vector bundles on a general quintic surface.

Findings

Moduli space is irreducible for c2 ≥ 16.

Provides explicit bound improving previous results.

Focuses on vector bundles with fixed Chern classes on a quintic surface.

Abstract

In this paper I consider a quintic surface in $\pp^3$, general in the sense of Noether-Lefschetz theory. The vector bundles of rank 2 on this surface which are $\mu$-stable with respect to the hyperplane section and have $c_1 = K$, the canonical class of the surface and fixed $c_2$, are parametrized by a moduli space. This space is known to be irreducible for large $c_2$ (work of K.G. O'Grady). I give an explicit bound, namely $c_2 \geq 16$.