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Differential Forms and Smoothness of Quotients by Reductive Groups

Published online by Cambridge University Press:  04 December 2007

Guillaume Jamet
Guillaume Jamet
Affiliation:
Institut de Mathématiques de Jussieu–Université Pierre et Marie Curie, Paris, 75252 Paris Cedex, France. e-mail: jamet@math.jussieu.fr
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Abstract

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Let π : X [xlarr ] Y be a good quotient of a smooth variety X by a reductive algebraic group G and 1[les ]k≤ dim (Y) an integer. We prove that if, locally, any invariant horizontal differential k-form on X (resp. any regular differential k-form on Y) is a Kähler differential form on Y then codim(Ysing)>k+1. We also prove that the dualizing sheaf on Y is the sheaf of invariant horizontal dim(Y)-forms.

Keywords

invariant theoryrational singularitiesfundamental classKähler differentials
Type
Research Article
Information
Compositio Mathematica , Volume 133 , Issue 2 , September 2002 , pp. 151 - 171
Copyright
© 2002 Kluwer Academic Publishers