Irreducibility of a universal Prym-Brill-Noether locus

TL;DR

This paper proves that for certain genera, the universal Prym-Brill-Noether locus has a unique irreducible component dominating the Prym moduli space, highlighting its fundamental geometric structure.

Contribution

It establishes the irreducibility of the universal Prym-Brill-Noether locus for specific genera, a key step in understanding its geometric properties.

Findings

Universal Prym-Brill-Noether locus is irreducible for genus g = r(r+1)/2 + 1.

Unique irreducible component dominates the Prym moduli space.

Results contribute to the understanding of Prym varieties and their moduli.

Abstract

For genus $g = \frac{r(r+1)}{2}+1$, we prove that via the forgetful map, the universal Prym-Brill-Noether locus $\mathcal{R}^r_g$ has a unique irreducible component dominating the moduli space $\mathcal{R}_g$ of Prym curves.