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Is the moduli space of Prym curves (curves $C$ with square root of $\mathcal{O}_C$, compactified via admissible covers - by Beauville) of a given genus $g$ normal? Why?

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up vote 3 down vote accepted

There are various references. The one I like is the following, particularly Remark 1.3.3.

MR2007376 (2005b:14049) Reviewed Abramovich, Dan(1-BOST); Corti, Alessio(4-CAMB); Vistoli, Angelo(I-BOLO) Twisted bundles and admissible covers. (English summary) Special issue in honor of Steven L. Kleiman. Comm. Algebra 31 (2003), no. 8, 3547–3618. 14H10 (14A20 14H30)

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The stack $\overline{\mathcal{P}}_{g}$ of Prym curves is a smooth Deligne-Mumford stack. This implies that its coarse moduli space $\overline{P}_{g}$ is normal with at most fine quotient singularities.

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