# normality of moduli of prym curves

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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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.