Spherical varieties and existence of invariant Kähler structures

previous :: next

Spherical varieties and existence of invariant Kähler structures

Chris T. Woodward

Source: Duke Math. J. Volume 93, Number 2 (1998), 345-377.

First Page: Show

Primary Subjects: 58F05

Secondary Subjects: 32C17

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077230884
Mathematical Reviews number (MathSciNet): MR1625995
Zentralblatt MATH identifier: 0979.53085
Digital Object Identifier: doi:10.1215/S0012-7094-98-09312-7

back to Table of Contents

References

[1] J. Arms, R. H. Cushman, and M. J. Gotay, A universal reduction procedure for Hamiltonian group actions, The Geometry of Hamiltonian Systems (Berkeley, Calif., 1989), Math. Sci. Res. Inst. Publ., vol. 22, Springer-Verlag, New York, 1991, pp. 33–51.

Mathematical Reviews (MathSciNet): MR92h:58059

Zentralblatt MATH: 0742.58016

[2] M. F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), no. 1, 1–15.

Mathematical Reviews (MathSciNet): MR83e:53037

Zentralblatt MATH: 0482.58013

Digital Object Identifier: doi:10.1112/blms/14.1.1

[3] M. F. Atiyah and R. Bott, The moment map and equivariant cohomology, Topology 23 (1984), no. 1, 1–28.

Mathematical Reviews (MathSciNet): MR85e:58041

Zentralblatt MATH: 0521.58025

Digital Object Identifier: doi:10.1016/0040-9383(84)90021-1

[4] M. Brion, Quelques propriétés des espaces homogènes sphériques, Manuscripta Math. 55 (1986), no. 2, 191–198.

Mathematical Reviews (MathSciNet): MR87g:14054

Zentralblatt MATH: 0604.14048

Digital Object Identifier: doi:10.1007/BF01168684

[5] M. Brion, Sur l'image de l'application moment, Séminaire d'algèbre Paul Dubreil et Marie-Paule Malliavin (Paris, 1986), Lecture Notes in Math., vol. 1296, Springer, Berlin, 1987, pp. 177–192.

Mathematical Reviews (MathSciNet): MR89i:32062

Zentralblatt MATH: 0667.58012

[6] M. Brion, Groupe de Picard et nombres caractéristiques des variétés sphériques, Duke Math. J. 58 (1989), no. 2, 397–424.

Mathematical Reviews (MathSciNet): MR90i:14048

Zentralblatt MATH: 0701.14052

Digital Object Identifier: doi:10.1215/S0012-7094-89-05818-3

Project Euclid: euclid.dmj/1077307531

[7] M. Brion, Spherical varieties: An introduction, Topological Methods in Algebraic Transformation Groups (New Brunswick, N.J., 1988) eds. H. Kraft, T. Petrie, and G. Schwarz, Progr. Math., vol. 80, Birkhäuser, Boston, 1989, pp. 11–26.

Mathematical Reviews (MathSciNet): MR90m:14050

Zentralblatt MATH: 0724.14034

[8] M. Brion, Vers une généralisation des espaces symétriques, J. Algebra 134 (1990), no. 1, 115–143.

Mathematical Reviews (MathSciNet): MR91i:14039

Zentralblatt MATH: 0729.14038

Digital Object Identifier: doi:10.1016/0021-8693(90)90214-9

[9] M. Brion, Sur la géométrie des variétés sphériques, Comment. Math. Helv. 66 (1991), no. 2, 237–262.

Mathematical Reviews (MathSciNet): MR93a:14043

Zentralblatt MATH: 0741.14027

Digital Object Identifier: doi:10.1007/BF02566646

[10] J. B. Carrell and D. I. Lieberman, Holomorphic vector fields and Kaehler manifolds, Invent. Math. 21 (1973), 303–309.

Mathematical Reviews (MathSciNet): MR48:4356

Zentralblatt MATH: 0253.32017

Digital Object Identifier: doi:10.1007/BF01418791

[11] T. Delzant, Hamiltoniens périodiques et images convexes de l'application moment, Bull. Soc. Math. France 116 (1988), no. 3, 315–339.

Mathematical Reviews (MathSciNet): MR90b:58069

Zentralblatt MATH: 0676.58029

[12] T. Delzant, Classification des actions hamiltoniennes complètement intégrables de rang deux, Ann. Global Anal. Geom. 8 (1990), no. 1, 87–112.

Mathematical Reviews (MathSciNet): MR92f:58078

Zentralblatt MATH: 0711.58017

Digital Object Identifier: doi:10.1007/BF00055020

[13] A. Foschi, On the combinatorics for wonderful varieties, preprint, Grenoble, 1996.

[14] R. Gompf, A new construction of symplectic manifolds, Ann. of Math. (2) 142 (1995), no. 3, 527–595.

Mathematical Reviews (MathSciNet): MR96j:57025

Zentralblatt MATH: 0849.53027

Digital Object Identifier: doi:10.2307/2118554

JSTOR: links.jstor.org

[15] R. Gompf and T. Mrowka, Irreducible $4$-manifolds need not be complex, Ann. of Math. (2) 138 (1993), no. 1, 61–111.

Mathematical Reviews (MathSciNet): MR95c:57053

Zentralblatt MATH: 0805.57012

Digital Object Identifier: doi:10.2307/2946635

JSTOR: links.jstor.org

[16] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley, New York, 1978.

Mathematical Reviews (MathSciNet): MR80b:14001

Zentralblatt MATH: 0408.14001

[17] V. Guillemin and E. Prato, Heckman, Kostant, and Steinberg formulas for symplectic manifolds, Adv. Math. 82 (1990), no. 2, 160–179.

Mathematical Reviews (MathSciNet): MR91h:58041

Zentralblatt MATH: 0718.58027

Digital Object Identifier: doi:10.1016/0001-8708(90)90087-4

[18] V. Guillemin and S. Sternberg, Multiplicity-free spaces, J. Differential Geom. 19 (1984), no. 1, 31–56.

Mathematical Reviews (MathSciNet): MR85h:58071

Zentralblatt MATH: 0548.58017

Project Euclid: euclid.jdg/1214438422

[19] V. Guillemin and S. Sternberg, The Gelfand-Cetlin system and quantization of the complex flag manifolds, J. Funct. Anal. 52 (1983), no. 1, 106–128.

Mathematical Reviews (MathSciNet): MR85e:58069

Zentralblatt MATH: 0522.58021

Digital Object Identifier: doi:10.1016/0022-1236(83)90092-7

[20] V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), no. 3, 515–538.

Mathematical Reviews (MathSciNet): MR83m:58040

Zentralblatt MATH: 0503.58018

Digital Object Identifier: doi:10.1007/BF01398934

[21] V. Guillemin and S. Sternberg, Symplectic Techniques in Physics, Cambridge Univ. Press, Cambridge, 1984.

Mathematical Reviews (MathSciNet): MR86f:58054

Zentralblatt MATH: 0576.58012

[22] A. Huckleberry and T. Wurzbacher, Multiplicity-free complex manifolds, Math. Ann. 286 (1990), no. 1-3, 261–280.

Mathematical Reviews (MathSciNet): MR91c:32027

Zentralblatt MATH: 0765.32016

Digital Object Identifier: doi:10.1007/BF01453576

[23] J. Humphreys, Reflection groups and Coxeter groups, Cambridge Stud. Adv. Math., vol. 29, Cambridge Univ. Press, Cambridge, 1990.

Mathematical Reviews (MathSciNet): MR92h:20002

Zentralblatt MATH: 0725.20028

[24] P. Iglesias, Les $\rm SO(3)$-variétés symplectiques et leur classification en dimension $4$, Bull. Soc. Math. France 119 (1991), no. 3, 371–396.

Mathematical Reviews (MathSciNet): MR92i:57023

Zentralblatt MATH: 0745.53027

[25] F. Knop, The Luna-Vust theory of spherical embeddings, Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), Manoj Prakashan, Madras, 1991, pp. 225–249.

Mathematical Reviews (MathSciNet): MR92m:14065

Zentralblatt MATH: 0812.20023

[26] F. Knop, The asymptotic behavior of invariant collective motion, Invent. Math. 116 (1994), no. 1-3, 309–328.

Mathematical Reviews (MathSciNet): MR94m:14063

Zentralblatt MATH: 0802.58024

Digital Object Identifier: doi:10.1007/BF01231563

[27] F. Knop, On the set of orbits for a Borel subgroup, Comment. Math. Helv. 70 (1995), no. 2, 285–309.

Mathematical Reviews (MathSciNet): MR96c:14039

Zentralblatt MATH: 0828.22016

Digital Object Identifier: doi:10.1007/BF02566009

[28] F. Knop, Automorphisms, root systems, and compactifications of homogeneous varieties, J. Amer. Math. Soc. 9 (1996), no. 1, 153–174.

Mathematical Reviews (MathSciNet): MR96c:14037

Zentralblatt MATH: 0862.14034

Digital Object Identifier: doi:10.1090/S0894-0347-96-00179-8

JSTOR: links.jstor.org

[29] F. Knop, Weyl groups of Hamiltonian manifolds, I, preprint; dg-ga/9712010.

[30] F. Knop, personal communication.

[31] F. Knop, H. Kraft, D. Luna, and T. Vust, Local properties of algebraic group actions, Algebraische Transformationsgruppen und Invariantentheorie eds. H. Kraft, P. Slodowy, and T. Springer, DMV Sem., vol. 13, Birkhäuser, Basel, 1989, pp. 63–75.

Mathematical Reviews (MathSciNet): MR1044585

Zentralblatt MATH: 0722.14032

[32] E. Lerman, Symplectic cuts, Math. Res. Lett. 2 (1995), no. 3, 247–258.

Mathematical Reviews (MathSciNet): MR96f:58062

Zentralblatt MATH: 0835.53034

[33] E. Lerman, E. Meinrenken, S. Tolman, and C. Woodward, Non-abelian convexity by symplectic cuts, preprint, M.I.T., 1995; dg-ga/9603015.

[34] D. Luna and Th. Vust, Plongements d'espaces homogènes, Comment. Math. Helv. 58 (1983), no. 2, 186–245.

Mathematical Reviews (MathSciNet): MR85a:14035

Zentralblatt MATH: 0545.14010

Digital Object Identifier: doi:10.1007/BF02564633

[35] D. McDuff, Remarks on the uniqueness of symplectic blowing up, Symplectic Geometry ed. D. Salamon, London Math. Soc. Lecture Note Ser., vol. 192, Cambridge Univ. Press, Cambridge, 1993, pp. 157–167.

Mathematical Reviews (MathSciNet): MR95h:57028

Zentralblatt MATH: 0822.53021

[36] D. McDuff and D. Salamon, Introduction to Symplectic Topology, Oxford Math. Monogr., Clarendon, Oxford Univ. Press, New York, 1995.

Mathematical Reviews (MathSciNet): MR97b:58062

Zentralblatt MATH: 0844.58029

[37] E. Meinrenken, Symplectic surgery and the $Spin_c-Dirac$ operator, to appear in Adv. Math.; dg-ga/9504002.

Mathematical Reviews (MathSciNet): MR1617809

Zentralblatt MATH: 0929.53045

Digital Object Identifier: doi:10.1006/aima.1997.1701

[38] G. W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 63–68.

Mathematical Reviews (MathSciNet): MR51:6870

Zentralblatt MATH: 0297.57015

Digital Object Identifier: doi:10.1016/0040-9383(75)90036-1

[39] R. Sjamaar, Holomorphic slices, symplectic reduction and multiplicities of representations, Ann. of Math. (2) 141 (1995), no. 1, 87–129.

Mathematical Reviews (MathSciNet): MR96a:58098

Zentralblatt MATH: 0827.32030

Digital Object Identifier: doi:10.2307/2118628

JSTOR: links.jstor.org

[40] R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction, Ann. of Math. (2) 134 (1991), no. 2, 375–422.

Mathematical Reviews (MathSciNet): MR92g:58036

Zentralblatt MATH: 0759.58019

Digital Object Identifier: doi:10.2307/2944350

JSTOR: links.jstor.org

[41] A. Thimm, Integrable geodesic flows on homogeneous spaces, Ergodic Theory Dynam. Systems 1 (1981), no. 4, 495–517.

Mathematical Reviews (MathSciNet): MR84d:58065

Zentralblatt MATH: 0491.58014

Digital Object Identifier: doi:10.1017/S0143385700001401

[42] S. Tolman, Examples of non-Kähler Hamiltonian torus actions, to appear in Invent. Math.

Mathematical Reviews (MathSciNet): MR1608575

Digital Object Identifier: doi:10.1007/s002220050205

[43] E. Vinberg, Complexity of actions of reductive groups, Funktsional. Anal. i Prilozhen. 20 (1986), no. 1, 1–13, 96.

Mathematical Reviews (MathSciNet): MR87j:14077

Zentralblatt MATH: 0601.14038

[44] C. Woodward, The classification of transversal multiplicity-free group actions, Ann. Global Anal. Geom. 14 (1996), no. 1, 3–42.

Mathematical Reviews (MathSciNet): MR97a:58067

Zentralblatt MATH: 0877.58022

Digital Object Identifier: doi:10.1007/BF00128193

[45] C. Woodward, Multiplicity-free Hamiltonian actions need not to be Käahler, to appear in Invent. Math.

Mathematical Reviews (MathSciNet): MR1608579

Digital Object Identifier: doi:10.1007/s002220050206

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?