Introduction to actions of algebraic groups

Michel Brion[1]

  • [1] Institut Fourier, B.P. 74 F-38402 Saint-Martin d’Hères Cedex

Les cours du CIRM (2010)

  • Volume: 1, Issue: 1, page 1-22
  • ISSN: 2108-7164

Abstract

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These notes present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures.

How to cite

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Brion, Michel. "Introduction to actions of algebraic groups." Les cours du CIRM 1.1 (2010): 1-22. <http://eudml.org/doc/116362>.

@article{Brion2010,
abstract = {These notes present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures.},
affiliation = {Institut Fourier, B.P. 74 F-38402 Saint-Martin d’Hères Cedex},
author = {Brion, Michel},
journal = {Les cours du CIRM},
keywords = {algebraic group action; Albanese morphism; almolst homogeneous varieties},
language = {eng},
number = {1},
pages = {1-22},
publisher = {CIRM},
title = {Introduction to actions of algebraic groups},
url = {http://eudml.org/doc/116362},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Brion, Michel
TI - Introduction to actions of algebraic groups
JO - Les cours du CIRM
PY - 2010
PB - CIRM
VL - 1
IS - 1
SP - 1
EP - 22
AB - These notes present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures.
LA - eng
KW - algebraic group action; Albanese morphism; almolst homogeneous varieties
UR - http://eudml.org/doc/116362
ER -

References

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  3. F. D. Grosshans, Algebraic Homogeneous Spaces and Invariant Theory, Lecture Notes in Math. 1673, Springer-Verlag, New York, 1997. Zbl0886.14020MR1489234
  4. R. Hartshorne, Algebraic Geometry, Graduate Texts Math. 52, Springer-Verlag, New York, 1977. Zbl0367.14001MR463157
  5. H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspects of Mathematics, Vieweg, Braunschweig/Wiesbaden, 1985. Zbl0569.14003MR768181
  6. F. Knop, H. Kraft, D. Luan and T. Vust, Local properties of algebraic group actions, in: Algebraic Transformation Groups and Invariant Theory, pp. 63–76, DMV Seminar Band 13, Birkhäuser, Basel, 1989. Zbl0722.14032MR1044585
  7. I. Losev, Uniqueness properties for spherical varieties, preprint, arXiv: 0904.2937. 
  8. S. Mukai, An Introduction to Invariants and Moduli, Cambridge Studies in Advanced Math. 81, Cambridge University Press, 2003. Zbl1033.14008MR2004218
  9. D. Mumford, J. Fogarty and F. Kirwan, Geometric invariant theory, third edition, Ergeb. Math. Grenzgebiete (2) 34, Springer-Verlag, Berlin, 1994. Zbl0797.14004MR1304906
  10. P. Orlik and L. Solomon, Singularities II: Automorphisms of Forms, Math. Ann. 231 (1978), 229–240. Zbl0352.14002MR476735
  11. V. L. Popov and E. B. Vinberg, Invariant theory, in: Algebraic Geometry IV, pp. 123–278, Encycl. Math. Sci. 55, Springer-Verlag, 1994. Zbl0789.14008
  12. G. W. Schwarz and M. Brion, Théorie des invariants & Géométrie des variétés quotient, Travaux en cours 51, Hermann, Paris, 2000. Zbl1095.14003
  13. T. A. Springer, Linear Algebraic Groups, Second edition, Progress in Math. 9, Birkhäuser, Basel, 1998. Zbl0927.20024MR1642713
  14. P. Tauvel and R. W. T. Yu, Lie Algebras and Algebraic Groups, Springer-Verlag, Berlin, 2005. Zbl1068.17001MR2146652

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