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Irreducibility of a universal Prym-Brill-Noether locus

Andrei Bud

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.

Irreducibility of a universal Prym-Brill-Noether locus

Abstract

For genus , we prove that via the forgetful map, the universal Prym-Brill-Noether locus has a unique irreducible component dominating the moduli space of Prym curves.
Paper Structure (2 sections, 2 theorems, 11 equations)

This paper contains 2 sections, 2 theorems, 11 equations.

Table of Contents

  1. Introduction
  2. Prym linear series

Key Result

Lemma 2.2

Let $[\pi\colon \widetilde{C}\rightarrow C]\in \overline{\mathcal{R}}_g$ with $\widetilde{C}$ of compact type and let $\overline{\mathcal{V}}^r_g$ the closure of $\mathcal{V}^r_g$ inside $\mathcal{G}^r_{2g-2}(\mathcal{R}_g)$. Then the fibre of the map $\overline{\mathcal{V}}^r_g\rightarrow \overline

Theorems & Definitions (4)

  • Definition 2.1
  • Lemma 2.2
  • Theorem 2.3
  • proof