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Geometry of Prym semicanonical pencils and an application to cubic threefolds

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  • Martí Lahoz
  • Juan Carlos Naranjo
  • Andrés Rojas

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.

Suggested Citation

  • Martí Lahoz & Juan Carlos Naranjo & Andrés Rojas, 2023. "Geometry of Prym semicanonical pencils and an application to cubic threefolds," Mathematische Nachrichten, Wiley Blackwell, vol. 296(7), pages 2918-2941, July.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:7:p:2918-2941
    DOI: 10.1002/mana.202100631
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