Cohomology of Quotients in Symplectic and Algebraic Geometry
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A01=Frances Clare Kirwan
Affine space
Algebraic closure
Algebraic geometry
Algebraic Method
Algebraic variety
Algebraically closed field
Author_Frances Clare Kirwan
Automorphism
Betti number
Category=PBF
Category=PBPD
Codimension
Cohomology
Complex manifold
Complex projective space
Complex vector bundle
Complexification
Complexification (Lie group)
Connected component (graph theory)
Degeneracy (mathematics)
Degenerate bilinear form
Differentiable manifold
Dimension (vector space)
Disjoint union
Endomorphism
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equivariant cohomology
Explicit formulae (L-function)
Exponential map (Lie theory)
Exterior algebra
Geometric invariant theory
Geometry
Grassmannian
Hodge theory
Homomorphism
Interval (mathematics)
Invariant theory
Kahler manifold
Lie algebra
Limit point
Linear algebraic group
Manifold decomposition
Mathematical induction
Maximal torus
Moduli space
Moment map
Morse theory
Open set
Polynomial
Projection (linear algebra)
Projective line
Projective linear group
Projective variety
Quasi-projective variety
Reductive group
Riemann sphere
Riemann surface
Riemannian manifold
Set (mathematics)
Sign (mathematics)
Special linear group
Subgroup
Submanifold
Subset
Symplectic geometry
Symplectic manifold
Symplectic vector space
Tangent space
Tensor algebra
Theorem
Variable (mathematics)
Vector bundle
Weil conjecture
Zariski topology
Product details
- ISBN 9780691083704
- Weight: 312g
- Dimensions: 152 x 235mm
- Publication Date: 21 Dec 1984
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
