Cohomology of Quotients in Symplectic and Algebraic Geometry

Cohomology of Quotients in Symplectic and Algebraic Geometry

Author: Frances Clare Kirwan

Publisher: Princeton University Press

ISBN: 9780691083704

Category: Mathematics

Page: 210

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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.
Cohomology of Quotients in Symplectic and Algebraic Geometry
Language: en
Pages: 210
Authors: Frances Clare Kirwan, John N. Mather, Phillip Griffiths
Categories: Mathematics
Type: BOOK - Published: 1984-12-21 - Publisher: Princeton University Press

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
Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31
Language: en
Pages: 216
Authors: Frances Clare Kirwan
Categories: Mathematics
Type: BOOK - Published: 2020-06-30 - Publisher: Princeton University Press

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
Minimal Surfaces, Geometric Analysis and Symplectic Geometry
Language: en
Pages: 259
Authors: Kenji Fukaya, Seiki Nishikawa, Joel Spruck
Categories: Mathematics
Type: BOOK - Published: 2002 - Publisher: Mathematical Soc of Japan

The 1998-1999 programme year of the Japan-U.S. Mathematics Institute at the Johns Hopkins University, USA was devoted to minimal surfaces, geometric analysis, and symplectic geometry. The programme culminated in a week-long workshop and conference to discuss developments. This volume is a collection of articles written by the speakers. It presents
Symplectic Geometry and Mathematical Physics
Language: en
Pages: 478
Authors: P. Donato, C. Duval, J. Elhadad, G.M. Tynman
Categories: Mathematics
Type: BOOK - Published: 1991-12 - Publisher: Springer Science & Business Media

This volume contains the proceedings of the conference "Colloque de Goometrie Symplectique et Physique Mathematique" which was held in Aix-en-Provence (France), June 11-15, 1990, in honor of Jean-Marie Souriau. The conference was one in the series of international meetings of the Seminaire Sud Rhodanien de Goometrie, an organization of geometers
The Geometry of Four-manifolds
Language: en
Pages: 440
Authors: Simon Kirwan Donaldson, S. K. Donaldson, P. B. Kronheimer
Categories: Fiction
Type: BOOK - Published: 1990 - Publisher: Oxford University Press

This text provides an accessible account to the modern study of the geometry of four-manifolds. Prerequisites are a firm grounding in differential topology and geometry, as may be gained from the first year of a graduate course.