Linked symplectic forms and limit linear series in rank 2 with special determinant

TL;DR

This paper extends linked symplectic Grassmannian techniques to establish smoothing, nonemptiness, and dimension results for rank-2 limit linear series with special determinants on chains of curves, advancing Brill-Noether theory.

Contribution

It introduces a generalized linked symplectic Grassmannian framework to analyze rank-2 limit linear series with fixed special determinants, leading to new smoothing and dimension results.

Findings

Proved smoothing of rank-2 limit linear series with special determinants.

Established nonemptiness of certain Brill-Noether loci.

Determined dimension bounds for rank-2 Brill-Noether loci.

Abstract

We generalize the prior linked symplectic Grassmannian construction, applying it to to prove smoothing results for rank-2 limit linear series with fixed special determinant on chains of curves. We apply this general machinery to prove new results on nonemptiness and dimension of rank-2 Brill-Noether loci in a range of degrees.