Geodesic
A generalization of Mumford's geometric invariant theory
Documenta mathematica, Tome 6 (2001), pp. 571-592.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We generalize Mumford's construction of good quotients for reductive group actions. Replacing a single linearized invertible sheaf with a certain group of sheaves, we obtain a Geometric Invariant Theory producing not only the quasiprojective quotient spaces, but more generally all divisorial ones. As an application, we characterize in terms of the Weyl group of a maximal torus, when a proper reductive group action on a smooth complex variety admits an algebraic variety as orbit space.
Classification : 14L24, 14L30
Keywords: geometric invariant theory, good quotients, reductive group actions 
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     author = {Hausen, J\"urgen},
     title = {A generalization of {Mumford's} geometric invariant theory},
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     volume = {6},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a0/}
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Hausen, Jürgen. A generalization of Mumford's geometric invariant theory. Documenta mathematica, Tome 6 (2001), pp. 571-592. http://geodesic.mathdoc.fr/item/DOCMA_2001__6__a0/