Center for diffusion of mathematic journals

 
 
 
 

Les cours du CIRM

Table of contents for this issue | Next article
Michel Brion
Introduction to actions of algebraic groups
Les cours du CIRM, 1 no. 1: Hamiltonian Actions: invariants et classification (2010), p. 1-22, doi: 10.5802/ccirm.1
Article PDF | 3 citations in Cedram

Résumé - 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.

Bibliography

[1] I. Dolgachev, Lectures on Invariant Theory, London Math. Soc. Lecture Note Series 296, Cambrigde University Press, 2003.  MR 2004511 |  Zbl 1023.13006
[2] W. Fulton, Introduction to Toric Varieties, Annals of Math. Studies 131, Princeton University Press, Princeton, 1993.  MR 1234037 |  Zbl 0813.14039
[3] F. D. Grosshans, Algebraic Homogeneous Spaces and Invariant Theory, Lecture Notes in Math. 1673, Springer-Verlag, New York, 1997.  MR 1489234 |  Zbl 0886.14020
[4] R. Hartshorne, Algebraic Geometry, Graduate Texts Math. 52, Springer-Verlag, New York, 1977.  MR 463157 |  Zbl 0367.14001
[5] H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspects of Mathematics, Vieweg, Braunschweig/Wiesbaden, 1985.  MR 768181 |  Zbl 0569.14003
[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.  MR 1044585 |  Zbl 0722.14032
[7] I. Losev, Uniqueness properties for spherical varieties, preprint, arXiv: 0904.2937.
arXiv
[8] S. Mukai, An Introduction to Invariants and Moduli, Cambridge Studies in Advanced Math. 81, Cambridge University Press, 2003.  MR 2004218 |  Zbl 1033.14008
[9] D. Mumford, J. Fogarty and F. Kirwan, Geometric invariant theory, third edition, Ergeb. Math. Grenzgebiete (2) 34, Springer-Verlag, Berlin, 1994.  MR 1304906 |  Zbl 0797.14004
[10] P. Orlik and L. Solomon, Singularities II: Automorphisms of Forms, Math. Ann. 231 (1978), 229–240.  MR 476735 |  Zbl 0352.14002
[11] V. L. Popov and E. B. Vinberg, Invariant theory, in: Algebraic Geometry IV, pp. 123–278, Encycl. Math. Sci. 55, Springer-Verlag, 1994.  Zbl 0789.14008
[12] G. W. Schwarz and M. Brion, Théorie des invariants & Géométrie des variétés quotient, Travaux en cours 51, Hermann, Paris, 2000.  Zbl 1095.14003
[13] T. A. Springer, Linear Algebraic Groups, Second edition, Progress in Math. 9, Birkhäuser, Basel, 1998.  MR 1642713 |  Zbl 0927.20024
[14] P. Tauvel and R. W. T. Yu, Lie Algebras and Algebraic Groups, Springer-Verlag, Berlin, 2005.  MR 2146652 |  Zbl 1068.17001
Copyright Cellule MathDoc 2014 | Credit | Site Map