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

Published 5 Apr 2021 in math.AG | (2104.01718v2)

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 $\mathrm{Pic}\mathbb{Q}(\overline{\mathcal{C}^{n\mathcal{R}}_g)$.}