By Frances Clare Kirwan
These notes describe a basic strategy for calculating the Betti numbers of the projective quotient types that geometric invariant idea affiliates to reductive team activities on nonsingular advanced projective types. those quotient forms are attention-grabbing specifically as a result of their relevance to moduli difficulties in algebraic geometry. the writer describes varied ways to the matter. One is only algebraic, whereas the opposite makes use of the equipment of symplectic geometry and Morse concept, and includes extending classical Morse thought to yes degenerate functions.
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