Seminatural bundles of rank two, degree one and $c_2=10$ on a quintic surface

TL;DR

This paper investigates the structure of the moduli space of rank two, degree one stable bundles with second Chern class 10 on a general quintic surface, revealing a unique component with seminatural cohomology.

Contribution

It identifies a single irreducible component of the moduli space with seminatural cohomology and conjectures this is the only component for all stable bundles.

Findings

Single irreducible component with seminatural cohomology identified

Conjecture that this component is unique for all stable bundles

Advances understanding of moduli space structure on quintic surfaces

Abstract

In this paper we continue our study of the moduli space of stable bundles of rank two and degree 1 on a very general quintic surface. The goal in this paper is to understand the irreducible components of the moduli space in the first case in the "good" range, which is $c_2=10$. We show that there is a single irreducible component of bundles which have seminatural cohomology, and conjecture that this is the only component for all stable bundles.