Cohomology of quotients in symplectic and algebraic geometry

These notes describe a general procedure for calculating the Betti numbers of the projective "ient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties. These "ient varieties are interesting in particular because of the...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Kirwan, Frances Clare, 1959- (Author)
Format: Electronic eBook
Language:Inglés
Published: Princeton, N.J. : Princeton University Press, 1984.
Series:Mathematical notes (Princeton University Press) ; 31.
Subjects:
Group schemes (Mathematics)
Algebraic varieties.
Homology theory.
Symplectic manifolds.
Schémas en groupes.
Variétés algébriques.
Homologie.
Variétés symplectiques.
"ient variety.
Cohomological formulae.
Critical points.
Deligne calls.
Grassmannian.
Hodge numbers.
Jacobian matrices.
Lie algebra.
Morse function.
algebraic geometry.
cotangent bundles.
critical subsets.
denotes.
equivariantly perfect.
geometry.
integers.
invariant.
moment map.
monomials.
nonsingular variety.
rational cohomology.
semistable stratum.
subspace.
symplectic manifold.
Online Access:Texto completo
Table of Contents:
  • Cover Page
  • Title Page
  • Copyright Page
  • Contents
  • 1. Introduction
  • Part I. The symplectic approach
  • 2. The moment map
  • 3. Critical points for the square of the moment map
  • 4. The square of the moment map as a Morse function
  • 5. Cohomological formulae
  • 6. Complex group actions on Kahler manifolds
  • 7. Quotients of Kahler manifolds
  • 8. The relationship with geometric invariant theory
  • 9. Some remarks on non-compact manifolds
  • 10. Appendix. Morse theory extended to minimally degenerate functions
  • Part II . The algebraic approach
  • 11. The basic idea
  • 12. Stratifications over arbitrary algebraically closed fields
  • 13. The strata of a nonsingular variety
  • 14. Hodge numbers
  • 15. Calculating cohomology by counting points
  • 16. Examples
  • References

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