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hal-00389309, version 1

Group actions on affine cones

Takashi Kishimoto () 1, Yuri Prokhorov () 2, Mikhail Zaidenberg () 3

(2009-05-28)

Abstract: We address the following question: Determine the affine cones over smooth projective varieties which admit an action of a connected algebraic group different from the standard C*-action by scalar matrices and its inverse action. We show in particular that the affine cones over anticanonically embedded smooth del Pezzo surfaces of degree at least 4 possess such an action. A question by Flenner and the third author whether this is also true for cubic surfaces, occurs to be out of reach for our methods. Nevertheless, we provide a general geometric criterion that could be helpful also in this case.

  • 1:  Department of Mathematics, Faculty of Science, Saitama University
  • Saitama University
  • 2:  Department of Algebra, Faculty of Mathematics, Moscow State University
  • Moscow State University
  • 3:  Institut Fourier (IF)
  • CNRS : UMR5582 – Université Joseph Fourier - Grenoble I
  • Domain : Mathematics/Algebraic Geometry
  • Keywords : del Pezzo surface – affine cone – group action – automorphism group
  • Internal note : IF_PREPUB
  • Comment : 27p.
  • Available versions :  v1 (2009-05-28) v2 (2010-01-30)
 
  • hal-00389309, version 1
  • http://hal.archives-ouvertes.fr/hal-00389309
  • oai:hal.archives-ouvertes.fr:hal-00389309
  • From: Mikhail Zaidenberg <>
  • Submitted on: Thursday, 28 May 2009 15:22:20
  • Updated on: Thursday, 15 October 2009 13:47:59