Differential forms and smoothness of quotients by reductive groups

Details Differential forms and smoothness of quotients by reductive groups Differential forms and smoothness of quotients by reductive groups

2000-11-02

arxiv.org/abs/math/0011014v1

Mathematics

Algebraic Geometry

25 pages, Latex2e with xy-pic, submitted to Compositio Math

Scientific paper

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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