Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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?

share|improve this question

2 Answers 2

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) http://arxiv.org/pdf/math/0106211.pdf

share|improve this answer

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.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.