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

Nicole Mestrano and Carlos Simpson

Vol. 293 (2018), No. 1, 121–172

DOI: 10.2140/pjm.2018.293.121

Abstract

The moduli space $M\left(c_2\right)$ of stable rank-two vector bundles of degree one on a very general quintic surface $X\subset {\mathbb{P}}^3$ is irreducible for all $c_2\ge 4$ and empty otherwise. On the other hand, for a very general sextic surface, the moduli space at $c_2=11$ has at least two irreducible components.

Keywords

vector bundle, surface, moduli space, deformation, boundary

Mathematical Subject Classification 2010

Primary: 14D20

Secondary: 14H50, 14J29

Milestones

Received: 25 January 2017

Revised: 7 September 2017

Accepted: 11 September 2017

Published: 3 November 2017