The Geometry and Topology of Quotient Varieties
نویسندگان
چکیده
Let X be a nonsingular projective variety with an algebraic action of a complex torus (c*)n. We study in this thesis the symplectic quotients (reduced phase spaces) and the quotients in a more general sense. As a part of our program, we have developed a general procedure for computing the intersection homology groups of the quotient varieties. In particular, we obtained an explicit inductive formula for the intersection Poincare polynomial of an arbitrary quotient. Also, explicit resultswere obtained in the case of the maximal torus actions on the flag varieties G/ B. Thesis Supervisor: Robert MacPherson Title: Professor of Mathematics
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