Seminatural bundles of rank two, degree one, and c2=10 on a quintic surface

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 we conjecture that this is the only component for all stable bundles.