The fibers of the ramified Prym map

We study the ramified Prym map \(\mathcal P_{g,r} \longrightarrow \mathcal A_{g-1+\frac r2}^{\delta}\) which assigns to a ramified double cover of a smooth irreducible curve of genus \(g\) ramified in \(r\) points the Prym variety of the covering. We focus on the six cases where the dimension of the...

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Bibliographic Details
Published inarXiv.org
Main Authors Frediani, P, Naranjo, J C, Spelta, I
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 07.05.2021
Subjects
Mathematics - Algebraic Geometry
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Summary:We study the ramified Prym map \(\mathcal P_{g,r} \longrightarrow \mathcal A_{g-1+\frac r2}^{\delta}\) which assigns to a ramified double cover of a smooth irreducible curve of genus \(g\) ramified in \(r\) points the Prym variety of the covering. We focus on the six cases where the dimension of the source is strictly greater than the dimension of the target giving a geometric description of the generic fibre. We also give an explicit example of a totally geodesic curve which is an irreducible component of a fibre of the Prym map \({\mathcal P}_{1,2}\).
ISSN:2331-8422
DOI:10.48550/arxiv.2007.02068