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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, N.J. :
Princeton University Press,
1984.
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| Colección: | Mathematical notes (Princeton University Press) ;
31. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Kirwan, Frances Clare, |d 1959- |e author |1 http://viaf.org/viaf/87201 | |
| 245 | 1 | 0 | |a Cohomology of quotients in symplectic and algebraic geometry |c by Frances Clare Kirwan. |
| 264 | 1 | |a Princeton, N.J. : |b Princeton University Press, |c 1984. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
| 337 | |a computer |b c |2 rdamedia |0 http://id.loc.gov/vocabulary/mediaTypes/c | ||
| 338 | |a online resource |b cr |2 rdacarrier |0 http://id.loc.gov/vocabulary/carriers/cr | ||
| 490 | 1 | |a Mathematical notes ; |v 31 | |
| 504 | |a Bibliography: pages 208-210. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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 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. | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 650 | 0 | |a Group schemes (Mathematics) | |
| 650 | 0 | |a Algebraic varieties. | |
| 650 | 0 | |a Homology theory. | |
| 650 | 0 | |a Symplectic manifolds. | |
| 650 | 6 | |a Schémas en groupes. | |
| 650 | 6 | |a Variétés algébriques. | |
| 650 | 6 | |a Homologie. | |
| 650 | 6 | |a Variétés symplectiques. | |
| 650 | 7 | |a Symplectic manifolds. |2 fast |0 (OCoLC)fst01140991 | |
| 650 | 7 | |a Homology theory. |2 fast |0 (OCoLC)fst00959720 | |
| 650 | 7 | |a Group schemes (Mathematics) |2 fast |0 (OCoLC)fst00948511 | |
| 650 | 7 | |a Algebraic varieties. |2 fast |0 (OCoLC)fst00804944 | |
| 653 | |a "ient variety. | ||
| 653 | |a Cohomological formulae. | ||
| 653 | |a Critical points. | ||
| 653 | |a Deligne calls. | ||
| 653 | |a Grassmannian. | ||
| 653 | |a Hodge numbers. | ||
| 653 | |a Jacobian matrices. | ||
| 653 | |a Lie algebra. | ||
| 653 | |a Morse function. | ||
| 653 | |a algebraic geometry. | ||
| 653 | |a cotangent bundles. | ||
| 653 | |a critical subsets. | ||
| 653 | |a denotes. | ||
| 653 | |a equivariantly perfect. | ||
| 653 | |a geometry. | ||
| 653 | |a integers. | ||
| 653 | |a invariant. | ||
| 653 | |a moment map. | ||
| 653 | |a monomials. | ||
| 653 | |a nonsingular variety. | ||
| 653 | |a rational cohomology. | ||
| 653 | |a semistable stratum. | ||
| 653 | |a subspace. | ||
| 653 | |a symplectic manifold. | ||
| 776 | 0 | 8 | |i Print version: |a Kirwan, Frances Clare |t Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31 |d Princeton : Princeton University Press,c1984 |z 9780691083704 |
| 830 | 0 | |a Mathematical notes (Princeton University Press) ; |v 31. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctv10vm2m8 |z Texto completo |
| 938 | |a YBP Library Services |b YANK |n 16773909 | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH37443443 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL6214780 | ||
| 994 | |a 92 |b IZTAP | ||