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.
@article{CCIRM_2010__1_1_1_0,
author = {Michel Brion},
title = {Introduction to actions of algebraic groups},
journal = {Les cours du CIRM},
pages = {1--22},
publisher = {CIRM},
volume = {1},
number = {1},
year = {2010},
doi = {10.5802/ccirm.1},
language = {en},
url = {https://ccirm.centre-mersenne.org/articles/10.5802/ccirm.1/}
}
TY - JOUR TI - Introduction to actions of algebraic groups JO - Les cours du CIRM PY - 2010 DA - 2010/// SP - 1 EP - 22 VL - 1 IS - 1 PB - CIRM UR - https://ccirm.centre-mersenne.org/articles/10.5802/ccirm.1/ UR - https://doi.org/10.5802/ccirm.1 DO - 10.5802/ccirm.1 LA - en ID - CCIRM_2010__1_1_1_0 ER -
Michel Brion. Introduction to actions of algebraic groups. Les cours du CIRM, Volume 1 (2010) no. 1, pp. 1-22. doi : 10.5802/ccirm.1. https://ccirm.centre-mersenne.org/articles/10.5802/ccirm.1/
[1] I. Dolgachev, Lectures on Invariant Theory, London Math. Soc. Lecture Note Series 296, Cambrigde University Press, 2003.
[2] W. Fulton, Introduction to Toric Varieties, Annals of Math. Studies 131, Princeton University Press, Princeton, 1993.
[3] F. D. Grosshans, Algebraic Homogeneous Spaces and Invariant Theory, Lecture Notes in Math. 1673, Springer-Verlag, New York, 1997.
[4] R. Hartshorne, Algebraic Geometry, Graduate Texts Math. 52, Springer-Verlag, New York, 1977.
[5] H. Kraft, Geometrische Methoden in der Invariantentheorie, Aspects of Mathematics, Vieweg, Braunschweig/Wiesbaden, 1985.
[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.
[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.
[9] D. Mumford, J. Fogarty and F. Kirwan, Geometric invariant theory, third edition, Ergeb. Math. Grenzgebiete (2) 34, Springer-Verlag, Berlin, 1994.
[10] P. Orlik and L. Solomon, Singularities II: Automorphisms of Forms, Math. Ann. 231 (1978), 229–240.
[11] V. L. Popov and E. B. Vinberg, Invariant theory, in: Algebraic Geometry IV, pp. 123–278, Encycl. Math. Sci. 55, Springer-Verlag, 1994.
[12] G. W. Schwarz and M. Brion, Théorie des invariants & Géométrie des variétés quotient, Travaux en cours 51, Hermann, Paris, 2000.
[13] T. A. Springer, Linear Algebraic Groups, Second edition, Progress in Math. 9, Birkhäuser, Basel, 1998.
[14] P. Tauvel and R. W. T. Yu, Lie Algebras and Algebraic Groups, Springer-Verlag, Berlin, 2005.
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