Brill-Noether loci with fixed determinant in rank 2

TL;DR

This paper generalizes earlier results on Brill-Noether loci with fixed determinant in rank 2 vector bundles, using symplectic Grassmannians to analyze their dimensions across a broader range.

Contribution

It extends previous work by Bertram, Feinberg, and Mukai to a wider class of fixed-determinant Brill-Noether loci, employing symplectic Grassmannian techniques.

Findings

Dimension exceeds naive expectations in broader cases

Uses symplectic Grassmannians for analysis

Generalizes prior rank 2 results

Abstract

In the 1990's, Bertram, Feinberg and Mukai examined Brill-Noether loci for vector bundles of rank 2 with fixed canonical determinant, noting that the dimension was always bigger in this case than the naive expectation. We generalize their results to treat a much broader range of fixed-determinant Brill-Noether loci. The main technique is a careful study of symplectic Grassmannians and related concepts.