Transformation Groups

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




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.


Projective Variety Pezzo Surface Homogeneous Element Cartier Divisor Cone Versus 
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© Springer Science+Business Media New York 2013

Authors and Affiliations

    • 1
    Email author
    • 2
    • 3
    • 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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