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arXiv · 2104.01718

The birational geometry of $\overline{\mathcal{R}}_{g,2}$ and Prym-canonical divisorial strata

Andrei Bud
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Abstract

We prove that the moduli space of double covers ramified at two points $\mathcal{R}_{g,2}$ is uniruled for $3\leq g\leq 6$ and of general type for $g\geq 16$. Furthermore, we consider Prym-canonical divisorial strata in the moduli space $\overline{\mathcal{C}^n\mathcal{R}}_g$ parametrizing $n$-pointed Prym curves, and we compute their classes in $\mathrm{Pic}_\mathbb{Q}(\overline{\mathcal{C}^n\mathcal{R}}_g)$.

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Andrei Bud. 2021-04-05. The birational geometry of $\overline{\mathcal{R}}_{g,2}$ and Prym-canonical divisorial strata. https://arxiv.org/abs/2104.01718

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