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Geometric Invariant Theory based on Weil divisors

Published online by Cambridge University Press:  15 October 2004

Jürgen Hausen
Jürgen Hausen
Affiliation:
Mathematisches Forschungsinstitut Oberwolfach, Schwarzwaldstraße 9-11, 77709 Oberwolfach-Walke, Germanyhausen@mfo.de
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Abstract

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Given an action of a reductive group on a normal variety, we describe all invariant open subsets admitting a good quotient with a quasiprojective or a divisorial quotient space. We obtain several new Hilbert–Mumford type theorems, and we extend a projectivity criterion of Białynicki-Birula and Święcicka for varieties with semisimple group action from the smooth to the singular case.

Keywords

reductive group actionlinearizationgood quotientHilbert–Mumford theorems14L2414L30
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 6 , November 2004 , pp. 1518 - 1536
Copyright
Foundation Compositio Mathematica 2004