# On the locus of Prym curves where the Prym--canonical map is not an embedding

## TL;DR

This paper characterizes the geometric locus of Prym curves where the Prym-canonical map fails to be an embedding, proving it is irreducible and unirational with a specific dimension for genus g ≥ 5.

## Contribution

It establishes the irreducibility and unirationality of the locus of Prym curves with non-embedding Prym-canonical maps for genus g ≥ 5.

## Key findings

- Locus is irreducible for g ≥ 5
- Locus is unirational for g ≥ 5
- Dimension of the locus is 2g+1

## Abstract

We prove that the locus of Prym curves $(C,\eta)$ of genus $g \geq 5$ for which the Prym-canonical system $|\omega_C(\eta)|$ is base point free but the Prym--canonical map is not an embedding is irreducible and unirational of dimension $2g+1$.