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arXiv · 2106.08683

Geometry of Prym semicanonical pencils and an application to cubic threefolds

Martí Lahoz·Juan Carlos Naranjo·Andrés Rojas
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Abstract

In the moduli space $\mathcal{R}_g$ of double \'etale covers of curves of a fixed genus $g$, the locus formed by covers of curves with a semicanonical pencil consists of two irreducible divisors $\mathcal T^e_g$ and $\mathcal T^o_g$. 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 $\mathcal T^o_5$ has enumerative consequences for lines on cubic threefolds.

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Martí Lahoz, Juan Carlos Naranjo, Andrés Rojas. 2021-06-16. Geometry of Prym semicanonical pencils and an application to cubic threefolds. https://doi.org/10.1002/mana.202100631

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