Geometric Invariant Theory via Cox Rings

Details Geometric Invariant Theory via Cox Rings Geometric Invariant Theory via Cox Rings

2007-06-29

arxiv.org/abs/0706.4353v2

J. Pure Appl. Algebra 213, 154-172 (2009)

Mathematics

Algebraic Geometry

27 pages, minor changes, Example 8.8 replaced, to appear in Journal of Pure and Applied Algebra

Scientific paper

We consider actions of reductive groups on a varieties with finitely generated Cox ring, e.g., the classical case of a diagonal action on a product of projective spaces. Given such an action, we construct via combinatorial data in the Cox ring all maximal open subsets such that the quotient is quasiprojective or embeddable into a toric variety. As applications, we obtain an explicit description of the chamber structure of the linearized ample cone and several Gelfand-MacPherson type correspondences relating quotients of reductive groups to quotients of torus actions. Moreover, our approach provides information on the geometry of many of the resulting quotient spaces.

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