Differential forms and smoothness of quotients by reductive groups

Guillaume Jamet

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arXiv · math/0011014

Differential forms and smoothness of quotients by reductive groups

Guillaume Jamet

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Abstract

In this paper we give smoothness criterions for a good quotient Y of a smooth variety X by a reductive group G. Our results partially answer a question raised by J. Fogarty in the case where G is a finite group. They also give a converse to a theorem of M. Brion, telling that invariant horizontal differential forms on X and differential forms on Y are isomorphic under the assumption that Y is smooth. The proof of our criterion rely on a new description of the dualizing sheaf of Y established in this article.

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BibTeX RIS

Guillaume Jamet. 2000-11-02. Differential forms and smoothness of quotients by reductive groups. https://arxiv.org/abs/math/0011014

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