Geometry of Prym semicanonical pencils and an application to cubic threefolds

Martí Lahoz, Juan Carlos Naranjo and Andrés Rojas

Mathematische Nachrichten, 2023, vol. 296, issue 7, 2918-2941

Abstract: In the moduli space Rg$\mathcal {R}_g$ 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 Tge$\mathcal {T}^e_g$ and Tgo$\mathcal {T}^o_g$. 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 T5o$\mathcal {T}^o_5$ has enumerative consequences for lines on cubic threefolds.

Date: 2023
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