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Geometry of Prym semicanonical pencils and an application to cubic threefolds (2106.08683v2)

Published 16 Jun 2021 in math.AG

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 $\mathcal Te_g$ and $\mathcal To_g$. 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 $\mathcal To_5$ has enumerative consequences for lines on cubic threefolds.

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