Geometric Invariant Theory based on Weil Divisors

Details Geometric Invariant Theory based on Weil Divisors Geometric Invariant Theory based on Weil Divisors

2003-01-19

arxiv.org/abs/math/0301204v2

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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