A generalization of Mumford's geometric invariant theory
Jürgen Hausen
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Abstract
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.
Cite this article
Jürgen Hausen, A generalization of Mumford's geometric invariant theory. Doc. Math. 6 (2001), pp. 571–592
DOI 10.4171/DM/114