Abstract
Moduli spaces of stable pointed curves can be represented as quotients M=X/G, where X is a smooth variety and G a finite group. This is an important fact, since varieties of this kind, even when singular, have a naturally defined intersection theory. We describe this quotient representation, starting from the case of smooth curves where the constructions are considerably more transparent from a geometrical point of view. Using the theory of admissible covers, we then treat the quotient representation of the compactified moduli spaces. In this case, in order to prove that the variety X is smooth at points of its boundary, the fundamental tool is the Picard–Lefschetz theory and the study of the local monodromy action.
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© 2011 Springer-Verlag Berlin Heidelberg
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Arbarello, E., Cornalba, M., Griffiths, P.A. (2011). Smooth Galois covers of moduli spaces. In: Geometry of Algebraic Curves. Grundlehren der mathematischen Wissenschaften, vol 268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69392-5_8
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DOI: https://doi.org/10.1007/978-3-540-69392-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42688-2
Online ISBN: 978-3-540-69392-5
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