Excess dimensions for Brill-Noether schemes of stable vector bundles

TL;DR

This paper extends classical results in Brill-Noether theory and secant loci to the setting of stable vector bundles of higher rank, providing new insights into the geometry of their moduli spaces.

Contribution

It generalizes existing results from line bundles to higher rank stable vector bundles, revealing new geometric properties of Brill-Noether loci.

Findings

Extended classical Brill-Noether results to higher rank bundles

Derived new geometric consequences for moduli spaces

Enhanced understanding of secant loci in vector bundle theory

Abstract

We extend a result by Fulton-Harris-Lazarsfeld in Brill-Noehter theory of line bundles and, as well, a result by Aprod-Sernesi in theory of Secant Loci, to the Brill-Noehter locus of stable bundles inside the moduli space of higher rank stable vector bundles on a smooth projective algebraic curve. We give some consequences of this extended result.