On quasihomogeneous manifolds – via Brion-Luna-Vust theorem

Marco Andreatta; Jarosław A. Wiśniewski

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 3, page 531-544
  • ISSN: 0392-4041

Abstract

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We consider a smooth projective variety X on which a simple algebraic group G acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of G with the induced action of G on the normal bundle of a closed orbit of the action. We get effective results in case G = S ⁢ L ⁢ n and dim ⁡ X ≤ 2 ⁢ n - 2 .

How to cite

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Andreatta, Marco, and Wiśniewski, Jarosław A.. "On quasihomogeneous manifolds – via Brion-Luna-Vust theorem." Bollettino dell'Unione Matematica Italiana 6-B.3 (2003): 531-544. <http://eudml.org/doc/196189>.

@article{Andreatta2003,
abstract = {We consider a smooth projective variety $X$ on which a simple algebraic group $G$ acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of $G$ with the induced action of $G$ on the normal bundle of a closed orbit of the action. We get effective results in case $G=SL(n)$ and $\dim X \leq 2n-2$.},
author = {Andreatta, Marco, Wiśniewski, Jarosław A.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {531-544},
publisher = {Unione Matematica Italiana},
title = {On quasihomogeneous manifolds – via Brion-Luna-Vust theorem},
url = {http://eudml.org/doc/196189},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Andreatta, Marco
AU - Wiśniewski, Jarosław A.
TI - On quasihomogeneous manifolds – via Brion-Luna-Vust theorem
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/10//
PB - Unione Matematica Italiana
VL - 6-B
IS - 3
SP - 531
EP - 544
AB - We consider a smooth projective variety $X$ on which a simple algebraic group $G$ acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of $G$ with the induced action of $G$ on the normal bundle of a closed orbit of the action. We get effective results in case $G=SL(n)$ and $\dim X \leq 2n-2$.
LA - eng
UR - http://eudml.org/doc/196189
ER -

References

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  11. NAKANO, T., On equivariant completions of 3-dimensional homogeneous spaces of S ⁢ L ⁢ 2 , C , Japanese J. of Math., 15 (1989), 221-273. Zbl0721.14008MR1039245
  12. NAKANO, T., On quasi-homogeneous fourfolds of S ⁢ L ⁢ 3 , C , Osaka J. Math., 29 (1992), 719-733. Zbl0788.14046MR1192737
  13. OKONEK, C.- SCHNEIDER, M.- SPINDLER, H., Vector bundles on complex projective spaces, Progress in Math.3, Birkhäuser1980. Zbl0438.32016MR561910
  14. SZUREK, M.- WIŚNIEWSKI, J. A., On Fano manifolds, which are P k -bundles over P 2 , Nagoya Math. J., 120 (1990), 89-101. Zbl0728.14037MR1086572
  15. SLODOWY, P., Simple singularities and simple algebraic groups, SpringerLecture Notes in Math., 815 (1980). Zbl0441.14002MR584445
  16. TITS, J., Sur certaines classes d'espaces homogenés de groups de Lie, Mem. Ac. Roy. Belg., 29 (1955). Zbl0067.12301MR76286

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