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arXiv · 2103.01687

The divisors of Prym semicanonical pencils

Carlos Maestro Pérez·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 of covers of curves with a semicanonical pencil decomposes as the union of two divisors $\mathcal{T}^e_g$ and $\mathcal{T}^o_g$. Adapting arguments of Teixidor for the divisor of curves having a semicanonical pencil, we prove that both divisors are irreducible and compute their divisor classes in the Deligne-Mumford compactification $\overline{\mathcal{R}}_g$.

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Carlos Maestro Pérez, Andrés Rojas. 2021-03-02. The divisors of Prym semicanonical pencils. https://arxiv.org/abs/2103.01687

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