Irreducibility of a Universal Prym–Brill–Noether Locus

Abstract

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