Some examples of vector bundles in the base locus of the generalized theta divisor

TL;DR

This paper investigates the size of the base locus of the generalized theta divisor on moduli spaces of semi-stable vector bundles, demonstrating it is large for high rank and multiples of the divisor, extending previous degree-zero results.

Contribution

It extends known results about the base locus of the theta divisor to cases with arbitrary degree determinants and higher ranks.

Findings

The base locus is large for sufficiently high rank vector bundles.

The base locus remains large for positive multiples of the theta divisor.

Results generalize previous degree-zero cases.

Abstract

This paper shows that on the moduli space of semi-stable vector bundles of fixed rank and determinant (of any degree) on a smooth curve of genus at least two, the base locus of the generalized theta divisor is large provided the rank is sufficiently large. It also shows that the base locus is large for positive multiples of the theta divisor. This work extends results already known for the case where the determinant is of degree zero.