Arkiv för Matematik

Volume 58 (2020)

Number 1

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

Pages: 71 – 85



Ciro Ciliberto (Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy)

Thomas Dedieu (Institut de Mathématiques de Toulouse, Université de Toulouse, France)

Concettina Galati (Dipartimento di Matematica e Informatica, Università della Calabria, Arcavacata di Rende (CS), Italy)

Andreas Leopold Knutsen (Department of Mathematics, University of Bergen, Norway)


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

Version Information: In the published form of the paper, the proof of Proposition 3.1 is incomplete. For the complete proof, see the Addendum in the arXiv version (arXiv:1903.05702) of this paper.

Received 24 June 2019

Received revised 13 November 2019

Accepted 25 November 2019

Published 21 July 2022