On compact orbits in singular Kähler spaces

Jörg Winkelmann

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1997)

  • Volume: 8, Issue: 1, page 31-38
  • ISSN: 1120-6330

Abstract

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For a complex solvable Lie group acting holomorphically on a Kähler manifold every closed orbit is isomorphic to a torus and any two such tori are isogenous. We prove a similar result for singular Kähler spaces.

How to cite

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Winkelmann, Jörg. "On compact orbits in singular Kähler spaces." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.1 (1997): 31-38. <http://eudml.org/doc/244153>.

@article{Winkelmann1997,
abstract = {For a complex solvable Lie group acting holomorphically on a Kähler manifold every closed orbit is isomorphic to a torus and any two such tori are isogenous. We prove a similar result for singular Kähler spaces.},
author = {Winkelmann, Jörg},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Kähler manifold; Solvable group; Isogenous tori; singular Kähler space; solvable complex Lie group; Albanese variety; torus},
language = {eng},
month = {4},
number = {1},
pages = {31-38},
publisher = {Accademia Nazionale dei Lincei},
title = {On compact orbits in singular Kähler spaces},
url = {http://eudml.org/doc/244153},
volume = {8},
year = {1997},
}

TY - JOUR
AU - Winkelmann, Jörg
TI - On compact orbits in singular Kähler spaces
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/4//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 1
SP - 31
EP - 38
AB - For a complex solvable Lie group acting holomorphically on a Kähler manifold every closed orbit is isomorphic to a torus and any two such tori are isogenous. We prove a similar result for singular Kähler spaces.
LA - eng
KW - Kähler manifold; Solvable group; Isogenous tori; singular Kähler space; solvable complex Lie group; Albanese variety; torus
UR - http://eudml.org/doc/244153
ER -

References

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  12. REMMERT, R. - VAN DE VEN, T., Zur Funktionentheorie homogener komplexer Mannigfaltigkeiten. Topology, 2, 1963, 137-157. Zbl0122.08602MR148085
  13. SNOW, D., Transformation groups of compact Kähler spaces. Arch. Math., 37, 1981, 364-371. Zbl0456.57017MR639342DOI10.1007/BF01234370
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  16. VAROUCHAS, J., Kähler spaces and proper open morphisms. Math. Ann., 283, no. 1, 1989, 13-52. Zbl0632.53059MR973802DOI10.1007/BF01457500
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