Mathematics – Algebraic Geometry
Scientific paper
2003-01-19
Compositio Math. 140, 1518-1536 (2004)
Mathematics
Algebraic Geometry
Final version, to appear in Compositio Math
Scientific paper
Given an action of a reductive group on a normal variety, we construct all invariant open subsets admitting a good quotient with a quasiprojective or a divisorial quotient space. Our approach extends known constructions like Mumford's Geometric Invariant Theory. We obtain several new Hilbert-Mumford type theorems, and we extend a projectivity criterion of Bialynicki-Birula and Swiecicka for varieties with semisimple group action from the smooth to the singular case.
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