Mathematische Zeitschrift

, Volume 282, Issue 3–4, pp 1067–1096 | Cite as

Primitive wonderful varieties

Article

Abstract

We complete the classification of wonderful varieties initiated by D. Luna. We review the results that reduce the problem to the family of primitive varieties, and report the references where some of them have already been studied. Finally, we analyze the rest case-by-case.

References

  1. 1.
    Ahiezer, D.N.: Equivariant completions of homogeneous algebraic varieties by homogeneous divisors. Ann. Glob. Anal. Geom. 1, 49-78 (1983)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bravi, P.: Wonderful varieties of type E. Represent. Theory 11, 174-191 (2007)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bravi, P.: Primitive spherical systems. Trans. Am. Math. Soc. 365, 361-407 (2013)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Bravi, P., Cupit-Foutou, S.: Classification of strict wonderful varieties. Ann. Inst. Fourier (Grenoble) 60, 641-681 (2010)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Bravi, P., Luna, D.: An introduction to wonderful varieties with many examples of type F4. J. Algebra 329, 4-51 (2011)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Bravi, P., Pezzini, G.: Wonderful varieties of type D. Represent. Theory 9, 578-637 (2005)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Bravi, P., Pezzini, G.: Wonderful subgroups of reductive groups and spherical systems. J. Algebra 409, 101-147 (2014)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Bravi, P., Pezzini, G.: The spherical systems of the wonderful reductive subgroups. J. Lie Theory 25(1), 105-123 (2015)MathSciNetMATHGoogle Scholar
  9. 9.
    Brion, M.: Classification des espaces homogènes sphériques. Compos. Math. 63, 189-208 (1987)MathSciNetGoogle Scholar
  10. 10.
    M. Brion, On spherical varieties of rank one (after D. Ahiezer, A. Huckleberry, D. Snow), Group actions and invariant theory (Montreal, PQ, 1989), CMS Conf. Proc., 10, Amer. Math. Soc. Providence, RI, pp. 31-41 (1988)Google Scholar
  11. 11.
    Cupit-Foutou, S.: Wonderful varieties: a geometrical realization. arXiv:0907.2852v3Google Scholar
  12. 12.
    De Concini, C., Procesi, C.: Complete symmetric varieties. In: Gherardelli, F. (ed.) Invariant Theory, Proceedings, Montecatini. Lect. Notes Math. 996, pp. 1-44. Springer, Berlin (1983)Google Scholar
  13. 13.
    Knop, F.: The Luna-Vust theory of spherical embeddings. In: Proceedings of the Hyderabad Conference on Algebraic Groups (Hyderabad, 1989), pp. 225-249, Manoj Prakashan, Madras (1991)Google Scholar
  14. 14.
    Knop, F.: The assymptotic behaviour of invariant collective motion. Invent. Math. 114, 309-328 (1994)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Knop, F.: Automorphisms, root systems, and compactifications of homogeneous varieties. J. Am. Math. Soc. 9, 153-174 (1996)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Krämer, M.: Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen. Compositio Math. 38, 129-153 (1979)MathSciNetMATHGoogle Scholar
  17. 17.
    Losev, I.V.: Uniqueness property for spherical homogeneous spaces. Duke Math. J. 147, 315-343 (2009)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Luna, D.: Toute variété magnifique est sphérique. Transform. Groups 1(3), 249-258 (1996)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Luna, D.: Variétés sphériques de type A. Publ. Math. Inst. Hautes Études Sci. 94, 161-226 (2001)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Mikityuk, I.V.: Integrability of invariant Hamiltonian systems with homogeneous configuration spaces. Math. USSR-Sb. 57, 527-546 (1987)CrossRefMATHGoogle Scholar
  21. 21.
    Pezzini, G.: Wonderful varieties of type C, Ph.D. Thesis, Università La Sapienza, Rome (2004)Google Scholar
  22. 22.
    Timashev, D.: Homogeneous spaces and equivariant embeddings. In: Encycl. Math. Sci., vol. 138. Springer, Berlin (2011)Google Scholar
  23. 23.
    Wasserman, B.: Wonderful varieties of rank two. Transform. Groups 1, 375-403 (1996)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità La SapienzaRomaItaly
  2. 2.Department MathematikFAU Erlangen-NürnbergErlangenGermany

Personalised recommendations