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

Abstract

We prove that the locus of Prym curves $(C,\eta )$ of genus $g\ge 5$ 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 $2g+1$.

Final version. The proof of Prop. 3.1. required additional arguments, now provided in an addendum

References in corpus (1)

• Moduli of curves on Enriques surfaces

Cited by in corpus (1)

• Kirchhoff's theorem for Prym varieties