Description

These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties. These quotient varieties are interesting in particular because of their relevance to moduli problems in algebraic geometry. The author describes two different approaches to the problem. One is purely algebraic, while the other uses the methods of symplectic geometry and Morse theory, and involves extending classical Morse theory to certain degenerate functions.

Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31

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These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory... Read more

    Publisher: Princeton University Press
    Publication Date: 21/12/1984
    ISBN13: 9780691083704, 978-0691083704
    ISBN10: 0691083703

    Number of Pages: 216

    Non Fiction , Mathematics & Science , Education

    Description

    These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties. These quotient varieties are interesting in particular because of their relevance to moduli problems in algebraic geometry. The author describes two different approaches to the problem. One is purely algebraic, while the other uses the methods of symplectic geometry and Morse theory, and involves extending classical Morse theory to certain degenerate functions.

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