Brill-Noether loci on an Enriques surface covered by a Jacobian Kummer surface

TL;DR

This paper constructs specific Brill-Noether loci within moduli spaces of stable rank 2 vector bundles on an Enriques surface covered by a Jacobian Kummer surface, revealing new geometric structures.

Contribution

It identifies proper first Brill-Noether loci inside moduli spaces of stable vector bundles on a special class of algebraic surfaces, providing explicit geometric examples.

Findings

Existence of proper Brill-Noether loci on Enriques surfaces

Construction of these loci within specific moduli spaces

Insights into the geometry of vector bundles on complex surfaces

Abstract

The aim of this note is to exhibit proper first Brill-Noether loci inside the moduli spaces $M_{Y,H}(2;c_1,c_2)$ of $H$-stable rank $2$ vector bundles with fixed Chern classes of a certain type on an Enriques surface $Y$ which is covered by a Jacobian Kummer surface $X$.