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Quotients of toric varieties. (English) Zbl 0762.14023
In geometric invariant theory actions of algebraic groups on projective varieties are studied. Mumford’s methods for the construction of quotients of such group actions do not in general lead to a unique or canonical quotient, rather to an inverse system of quotients. To remedy this situation the authors introduce the — canonical — Chow quotient. This quotient is thoroughly explored for the case that the variety under consideration is toric. Connections with the quotients obtained from geometric invariant theory are discussed.

MSC:
14M17 Homogeneous spaces and generalizations
14L30 Group actions on varieties or schemes (quotients)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14L24 Geometric invariant theory
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References:
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