Geometry of Prym semicanonical pencils and an application to cubic threefolds

Abstract

In the moduli space ${\mathcal{R}}_g$ of double étale covers of curves of a fixed genus $g$, the locus formed by covers of curves with a semicanonical pencil consists of two irreducible divisors ${\mathcal{T}}_g^e$ and ${\mathcal{T}}_g^o$. We study the Prym map on these divisors, which shows significant differences between them and has a rich geometry in the cases of low genus. In particular, the analysis of ${\mathcal{T}}_5^o$ has enumerative consequences for lines on cubic threefolds.

Fixed an inaccuracy in Theorem A and Section 3, and improved the exposition. Final version, to appear in Mathematische Nachrichten

References in corpus (3)

• Global Prym-Torelli for double coverings ramified in at least 6 points
• Theta-duality on Prym varieties and a Torelli Theorem
• The fibers of the ramified Prym map