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...
| Autores: | , , |
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| 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 |
| 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. |
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