Geometry of Prym semicanonical pencils and an application to cubic threefolds

In the moduli space $\mathcal{R}_{\mathrm{g}}$ 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...

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Detalhes bibliográficos
Autores: Lahoz Vilalta, Martí, Naranjo del Val, Juan Carlos, Rojas, Andrés
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2023
País:España
Recursos:Universidad de Barcelona
Repositório:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/197448
Acesso em linha:https://hdl.handle.net/2445/197448
Access Level:Acceso aberto
Palavra-chave:Geometria algebraica
Corbes algebraiques
Varietats abelianes
Algebraic geometry
Algebraic curves
Abelian varieties
Descrição
Resumo:In the moduli space $\mathcal{R}_{\mathrm{g}}$ 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.