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hal-00463347, version 1

Flag varieties, toric varieties, and suspensions: Three instances of infinite transitivity

Ivan Arzhantsev (Author to contact preferably) 1, Karine Kuyumzhiyan (Author to contact preferably) 1, 2, Mikhail Zaidenberg () 2

(2010-03-11)

Abstract: We say that a group G acts infinitely transitively on a set X if for every natural n, the induced diagonal action of G is transitive on the cartesian m-th power of X with the diagonals removed. We describe three classes of affine algebraic varieties such that their automorphism groups act infinitely transitively on their smooth loci. The first class consists of affine cones over flag varieties, the second of non-degenerate affine toric varieties, and the third of iterated suspensions over affine varieties with infinitely transitive automorphism groups of a reinforced type.

  • 1:  Department of Algebra, Faculty of Mathematics, Moscow State University
  • Moscow State University
  • 2:  Institut Fourier (IF)
  • CNRS : UMR5582 – Université Joseph Fourier - Grenoble I
  • Domain : Mathematics/Algebraic Geometry
  • Keywords : Flag varieties – toric varieties – group actions – affine varieties – transitivity
  • Internal note : IF_PREPUB
  • Comment : 25p.
    arXiv:1003.3164
 
  • hal-00463347, version 1
  • http://hal.archives-ouvertes.fr/hal-00463347
  • oai:hal.archives-ouvertes.fr:hal-00463347
  • From: Mikhail Zaidenberg <>
  • Submitted on: Thursday, 11 March 2010 21:25:32
  • Updated on: Friday, 2 April 2010 16:58:48