By Frances Clare Kirwan

These notes describe a basic strategy for calculating the Betti numbers of the projective quotient types that geometric invariant concept affiliates to reductive crew activities on nonsingular complicated projective kinds. those quotient forms are attention-grabbing specifically due to their relevance to moduli difficulties in algebraic geometry. the writer describes diverse ways to the matter. One is solely algebraic, whereas the opposite makes use of the tools of symplectic geometry and Morse concept, and comprises extending classical Morse idea to convinced degenerate functions.

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