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Transformation Groups

, Volume 18, Issue 4, pp 1137–1153 | Cite as

𝔾a-ACTIONS ON AFFINE CONES

  • TAKASHI KISHIMOTOEmail author
  • YURI PROKHOROV
  • MIKHAIL ZAIDENBERG
Article

Abstract

An affine algebraic variety X is called cylindrical if it contains a principal Zariski dense open cylinder U ≃ Z × A1. A polarized projective variety (Y, H) is called cylindrical if it contains a cylinder U = Y \ supp D, where D is an effective Q-divisor on Y such that [D] ∈ Q+[H] in PicQ(Y ). We show that cylindricity of a polarized projective variety is equivalent to that of a certain Veronese affine cone over this variety. This gives a criterion of the existence of a unipotent group action on an affine cone.

Keywords

Projective Variety Pezzo Surface Homogeneous Element Cartier Divisor Cone Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • TAKASHI KISHIMOTO
    • 1
    Email author
  • YURI PROKHOROV
    • 2
    • 3
  • MIKHAIL ZAIDENBERG
    • 4
  1. 1.Department of Mathematics Faculty of ScienceSaitama UniversitySaitamaJapan
  2. 2.Steklov Mathematical InstituteMoscowRussia
  3. 3.Laboratory of Algebraic Geometry GU-HSEMoscowRussia
  4. 4.Institut Fourier, UMR 5582 CNRS-UJFUniversité Grenoble ISt. Martin d’Hères cédexFrance

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