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Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31
Frances Clare Kirwan
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Degenerate bilinear form, Projective linear group, Limit point, Submanifold, Algebraic variety, Algebraic closure, Symplectic geometry, Open set, Mathematical induction, Projective line, Tensor algebra, Differentiable manifold, Cohomology, Moment map, Homomorphism, Tangent space, Theorem, Quasi-projective variety, Symplectic vector space, Complex projective space, Explicit formulae (L-function), Symplectic manifold, Betti number, Interval (mathematics), Weil conjecture, Automorphism, Complex vector bundle, Complexification, Riemannian manifold, Equivariant cohomology, Zariski topology, Morse theory, Kähler manifold, Riemann surface, Algebraic Method, Exponential map (Lie theory), Projection (linear algebra), Moduli space, Codimension, Geometric invariant theory, Riemann sphere, Algebraic geometry, Complexification (Lie group), Degeneracy (mathematics), Polynomial, Special linear group, Lie algebra, Set (mathematics), Sign (mathematics), Vector bundle, Invariant theory, Hodge theory, Variable (mathematics), Grassmannian, Linear algebraic group, Subgroup, Dimension (vector space), Endomorphism, Reductive group, Geometry, Maximal torus, Disjoint union, Complex manifold, Exterior algebra, Affine space, Manifold decomposition, Algebraically closed field, Connected component (graph theory), Projective variety, Subset