Propriétés de convexité de l'application moment

Alain Bruguières

Séminaire Bourbaki (1985-1986)

  • Volume: 28, page 63-87
  • ISSN: 0303-1179

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Bruguières, Alain. "Propriétés de convexité de l'application moment." Séminaire Bourbaki 28 (1985-1986): 63-87. <http://eudml.org/doc/110071>.

@article{Bruguières1985-1986,
author = {Bruguières, Alain},
journal = {Séminaire Bourbaki},
keywords = {symplectic manifold; Lie group; moment map; stratification; Marsden- Weinstein reduction; algebraic geometry},
language = {fre},
pages = {63-87},
publisher = {Société Mathématique de France},
title = {Propriétés de convexité de l'application moment},
url = {http://eudml.org/doc/110071},
volume = {28},
year = {1985-1986},
}

TY - JOUR
AU - Bruguières, Alain
TI - Propriétés de convexité de l'application moment
JO - Séminaire Bourbaki
PY - 1985-1986
PB - Société Mathématique de France
VL - 28
SP - 63
EP - 87
LA - fre
KW - symplectic manifold; Lie group; moment map; stratification; Marsden- Weinstein reduction; algebraic geometry
UR - http://eudml.org/doc/110071
ER -

References

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  1. [A] M.F. Atiyah - Convexity and commuting Hamiltonians, Bull. London Math. Soc.14, 1-15 (1982). Zbl0482.58013MR642416
  2. [A-B] M.F. Atiyah et R. Bott - The yang - Mills equation over Riemann surfaces, Phil. Trans. Royal Soc. London, A 308, 523-615 (1982). Zbl0509.14014MR702806
  3. [A-B1] M.F. Atiyah et R. Bott - The moment map and equivariant cohomology, Topology, 23, n° 1, 1-28 (1984). Zbl0521.58025MR721448
  4. [B-V] N. Berline et M. Vergne - Zéros d'un champ de vecteurs et classes caractéristiques équivariantes, Duke Math. Journal50, N° 2, 539-549 (1983) Zbl0515.58007MR705039
  5. [BB] A. Bialynicki - Birula - Some theorems on actions of algebraic groups, Annals of Math.98, 480-497 (1973). Zbl0275.14007MR366940
  6. [BB-S] A. Bialynicki - Birula et J. Świecicka - Generalized moment functions and orbit spaces, Preprint. MR882422
  7. [D-H],[D-Hl] J.J. Duistermaat et G.J. Heckman - On the variation in the cohomology of the symplectic form of the reduced phase space, et addendum, Invent. Math.69, 259-268 (1982) et 72, 153-158 (1983). Zbl0503.58016MR674406
  8. [G-S] V. Guillemin et S. Sternberg - Symplectic techniques in physics, Cambridge University Press (1984). Zbl0576.58012MR770935
  9. [G-S1],[G-S2] V. Guillemin et S. Sternberg - Convexity properties of the moment mapping I et II, Invent. Math.67, 491-513 (1982) et 77, 533-546 (1984). Zbl0561.58015MR664117
  10. [H] W.H. Hesselink - Uniform instability in reductive groups, J. Reine Angew. Math.304, 74-96 (1978). Zbl0386.20020MR514673
  11. [K] G. Kempf - Instability in invariant theory, Ann. Math.108, 299-316 (1978). Zbl0406.14031MR506989
  12. [Ki] F.C. Kirwan - Cohomology of quotients in symplectic and algebraic geometry, Princeton University Press, Mathematical Notes31(1984). Zbl0553.14020MR766741
  13. [Ki1] F.C. Kirwan - Convexity properties of the moment mapping III, Invent. Math.77, 547-552 (1984). Zbl0561.58016MR759257
  14. [Ki2] F.C. Kirwan - Partial desingularisations of quotients of non singular varieties and their Betti numbers, preprint soumis à Ann. Math. Zbl0592.14011
  15. [Ki3] F.C. Kirwan - On spaces of maps from Riemann surfaces to Grassmannians and applications to the cohomology of moduli of vector bundles, preprint soumis à Acta. Math. 
  16. [Ki-L] F.C. Kirwan et R. Lee - Article en préparation. 
  17. [M-W] J. Marsden et A. Weinstein - Reduction of symplectic manifolds with symmetry, Reports on Math. Phys.5, 121-130 (1974). Zbl0327.58005MR402819
  18. [M] D. Mumford - Geometric invariant theory, Springer-Verlag (1965). Seconde édition : D. MUMFORD et J. FOGARTY (1982). Zbl0504.14008MR214602

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