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arXiv · 2007.02068

The fibers of the ramified Prym map

P. Frediani·J. C. Naranjo·I. Spelta
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Abstract

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 ${\mathcal P}_{1,2}$.

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P. Frediani, J. C. Naranjo, I. Spelta. 2020-07-04. The fibers of the ramified Prym map. https://doi.org/10.1142/s0219199721500309

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