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,η) of genus g ≥ 5 for which the Prym-canonical system |ωC(η)| is base point free but the Prym--canonical map is not an embedding is irreducible and unirational of dimension 2g+1.

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