Irreducibility of moduli of vector bundles over a very general sextic Surface

TL;DR

This paper proves that the moduli space of certain stable rank 2 sheaves on a very general sextic surface in projective 3-space is irreducible, advancing understanding of vector bundle moduli on complex surfaces.

Contribution

It establishes the irreducibility of the moduli space of $ ext{μ}$-stable rank 2 torsion free sheaves with fixed Chern classes on a very general sextic surface.

Findings

Moduli space of stable sheaves is irreducible for $c_2 \\ge 27$.

Focus on very general smooth sextic surfaces in $\\mathbb{P}^3$.

Results contribute to the classification of vector bundles on algebraic surfaces.

Abstract

Let $S$ be a very general smooth hypersurface of degree $6$ in $\mathbb{P}^3$. In this paper we will prove that the moduli space of $\mu$-stable rank $2$ torsion free sheaves with respect to hyperplane section having $c_1 = \mathcal{O}_S(1)$, with fixed $c_2 \ge 27$ is irreducible.