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

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 $2g+1$.Comment: Final version. The proof of Prop. 3.1. required additional arguments, now provided in an addendu