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Galois Covers of Moduli of Curves

Published online by Cambridge University Press:  04 December 2007

M. Boggi  and
M. Pikaart
M. Boggi
Affiliation:
Universiteit Utrecht, Postbus 80.010, 3508 TA Utrecht, the Netherlands. e-mail: boggi@math.uu.nl
M. Pikaart
Affiliation:
Universität-Gesamthochschule Essen, FB 6 Mathematik, Universitätsstr. 3, D-4300 Essen, Germany. e-mail: martin.pikaart@uni-essen.de
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Abstract

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Moduli spaces of pointed curves with some level structure are studied. We prove that for so-called geometric level structures, the levels encountered in the boundary are smooth if the ambient variety is smooth, and in some cases we can describe them explicitly. The smoothness implies that the moduli space of pointed curves (over any field) admits a smooth finite Galois cover. Finally, we prove that some of these moduli spaces are simply connected.

Keywords

Moduli of curvesRiemann surfaceTeichmüller theoryfundamental groupGalois covers
Type
Research Article
Information
Compositio Mathematica , Volume 120 , Issue 2 , January 2000 , pp. 171 - 191
Copyright
© 2000 Kluwer Academic Publishers