Pseudoconcave homogeneous manifolds

A. T. Huckleberry; D. Snow

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1980)

  • Volume: 7, Issue: 1, page 29-54
  • ISSN: 0391-173X

How to cite

top

Huckleberry, A. T., and Snow, D.. "Pseudoconcave homogeneous manifolds." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 7.1 (1980): 29-54. <http://eudml.org/doc/83831>.

@article{Huckleberry1980,
author = {Huckleberry, A. T., Snow, D.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {noncompact homogeneous manifolds; 0-concave complex-homogeneous manifold; linear cone},
language = {eng},
number = {1},
pages = {29-54},
publisher = {Scuola normale superiore},
title = {Pseudoconcave homogeneous manifolds},
url = {http://eudml.org/doc/83831},
volume = {7},
year = {1980},
}

TY - JOUR
AU - Huckleberry, A. T.
AU - Snow, D.
TI - Pseudoconcave homogeneous manifolds
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1980
PB - Scuola normale superiore
VL - 7
IS - 1
SP - 29
EP - 54
LA - eng
KW - noncompact homogeneous manifolds; 0-concave complex-homogeneous manifold; linear cone
UR - http://eudml.org/doc/83831
ER -

References

top
  1. [1] A. Andreotti, Théorèmes de dépendance algebrique sur les espaces complex pseudo-concaves, Bull. Soc. Math. France, 91 (1963), pp. 1-38. Zbl0113.06403MR152674
  2. [2] A. Andreotti - H. Grauert, Théorèmes de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France, 90 (1962), pp. 193-259. Zbl0106.05501MR150342
  3. [3] A. Andreotti - A. Huckleberry, Pseudoconcave Lie groups, Compositio Math., 25 (1972), pp. 109-115. Zbl0239.32018MR316752
  4. [4] A. Andreotti - Y.T. Siu, Projective imbeddings of pseudoconcave spaces, Ann. Scuola Norm. Sup. Pisa, (3), 24 (1970), pp. 231-278. Zbl0195.36901MR265633
  5. [5] M. Atiyah, Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc., 85 (1957), pp. 181-207. Zbl0078.16002MR86359
  6. [6] W. Barth - M. Otte, Über fast-uniform Untergruppen komplexer Liegruppen und auflösbare komplexe Mannigfaltigkeiten, Comment. Math. Helv., 44 (1969), pp. 269-281. Zbl0172.37804MR253382
  7. [7] A. Blanchard, Sur les variétès anatytiques complexes, Ann. Sci. École Norm. Sup., 73 (1956), pp. 157-262. Zbl0073.37503MR87184
  8. [8] S. Bochner - D. Montgomery, Groups on analytic manifolds, Ann. of Math., II. See 48 (1954), pp. 1147-1151. Zbl0030.07501MR22223
  9. [9] A. Borel, Kählerian coset spaces of semisimple Lie groups, Proc. Nat. Acad. Sci. U.S.A., 40 (1954), pp. 1147-1151. Zbl0058.16002MR77878
  10. [10] A. Borel - R. Remmert, Über kompakte homogene Kählersche Mannigfaltigkeiten, Math. Ann., 145 (1962), pp. 429-439. Zbl0111.18001MR145557
  11. [11] B. Gilligan - A. Huckleberry, Pseudoconcave homogeneous surfaces, Com- ment. Math. Helv., 53 (1978), pp. 429-438. Zbl0387.32014MR499337
  12. [12] H. Grauert, Über modifikationen und exzeptionelle analytische Mengen, Math. Ann., 146 (1962), pp. 331-368. Zbl0173.33004MR137127
  13. [13] H. Grauert - R. Remmert, Über kompakte homogene komplexe Mannigfaltigkeiten, Arch. Math. (Basel), 13 (1962), pp. 498-507. Zbl0118.37402MR145558
  14. [14] H. Hironaka, The resolution of singularities of an algebraic variety (characteristic zero), Ann. of Math., 79 (1964), pp. 109-236. Zbl0122.38603MR199184
  15. [15] A.T. Huckleberry, Über Funktionenkorper auf komplexen Mannigfaltnigkeite, Schr. Math. Inst. Univ. Munster, 2. Serie, Heft 9 (1975). Zbl0299.32019MR367304
  16. [16] A.T. Huckleberry - E. Oeljeklaus, A characterization of homogeneous cones, Math. Z. (to appear). Zbl0412.32030MR562587
  17. [17] A.T. Huckleberry - D. Snow, A classification of strictly pseudoconcave homogeneous manifolds (to appear). Zbl0464.32019
  18. [18] J. Humphreys, Linear algebraic groves (graduate texts in mathematics, vol. 21), Springer-Verlag (1975). Zbl0325.20039MR396773
  19. [19] N. Kuhlmann, Über holomorphe abbildungen komplexer Räume, Arch. Math. (Basel), 15 (1964), pp. 81-90. Zbl0122.08701MR171939
  20. [20] Y. Matsushima, Fibrés holomorphes sur un tore complex, Nagoya Math. J., 13 (1958). Zbl0095.36702MR102613
  21. [21] Y. Matsushima, Espaces homogènes de Stein des groupes de Lie complexes I, Nagoya Math. J., 16 (1960), pp. 205-218. Zbl0094.28201MR109854
  22. [22] A. Mizuhara, On a Λ1-bundle over an abelian variety which is almost homogeneous, Math. Japon., 16 (1971), pp. 105-114. Zbl0258.14016
  23. [23] A. Morimoto, Non-compact complex Lie groups without non-constant holomorphic functions, Proceedings of the Conference on Complex Analysis, Minneapolis (1964), pp. 256-272. Zbl0144.07902MR181702
  24. [24] B. Mumford, Algebraic geometry. I: Complex projective varieties, Springer-Verlag (1976). Zbl0356.14002MR453732
  25. [25] E. Oeljeklaus, Über fast homogene kompakte komplexe Mannigfaltigkeiten, Schr. Math. Inst. Univ. Münster. Zbl0196.09602
  26. [26] E. Oeljeklaus, Ein Hebbarkeitssatz für Automorphismengruppen kompakter komplexer Mannigfaltigkeiten, Math. Ann., 190 (1970), pp. 154-166. Zbl0195.36902MR279332
  27. [27] R. Remmert - R. Stein, Über die wesentlichen singularitaten analytischer Mengen, Math. Ann., 126 (1953), pp. 263-306. Zbl0051.06303MR60033
  28. [28] R. Remmert - T. Van De Ven, Zur Functionentheorie homogener komptexer Mannigfaltigkeiten, Topology, vol. 2, Pergamon Press (1963), pp. 137-157. Zbl0122.08602MR148085
  29. [29] H. Rossi, Vector fields on analytic spaces, Ann. of Math., 78, no. 3 (1963), pp. 455-467. Zbl0129.29701MR162973
  30. [30] H. Rossi, Homogeneous strongly pseudoconvex hypersurfaces, Rice Univ. Studies, 59, nos. 1, 2 (1973), pp. 131-145. Zbl0277.32011MR330514
  31. [31] J. Tits, Espaces homogenes complexes compacts, Comment. Math. Helv., 37 (1962), pp. 111-120. Zbl0108.36302MR154299
  32. [32] H.C. Wang, Closed manifolds with homogeneous complex structure, Amer. J. Math., 76 (1954), pp. 1-32. Zbl0055.16603MR66011
  33. [33] A. Weil, Introduction à l'étude des variétés Kählériennes, Hermann (1958). Zbl0137.41103MR111056

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.