Geodesic
A generalization of Mumford's geometric invariant theory
Documenta mathematica, Tome 6 (2001), pp. 571-592
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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.
DOI : 10.4171/dm/114
Classification : 14L24, 14L30
Mots-clés : geometric invariant theory, good quotients, reductive group actions 
@article{10_4171_dm_114,
     author = {J\"urgen Hausen},
     title = {A generalization of {Mumford's} geometric invariant theory},
     journal = {Documenta mathematica},
     pages = {571--592},
     year = {2001},
     volume = {6},
     doi = {10.4171/dm/114},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/114/}
}
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Jürgen Hausen. A generalization of Mumford's geometric invariant theory. Documenta mathematica, Tome 6 (2001), pp. 571-592. doi: 10.4171/dm/114

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