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𝔾a-ACTIONS ON AFFINE CONES

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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.

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Authors and Affiliations

  1. Department of Mathematics Faculty of Science, Saitama University, Saitama, 338-8570, Japan

    TAKASHI KISHIMOTO

  2. Steklov Mathematical Institute, Gubkina 8, Moscow, 119991, Russia

    YURI PROKHOROV

  3. Laboratory of Algebraic Geometry GU-HSE, Vavilova 7, Moscow, 117312, Russia

    YURI PROKHOROV

  4. Institut Fourier, UMR 5582 CNRS-UJF, Université Grenoble I, BP 74, 38402, St. Martin d’Hères cédex, France

    MIKHAIL ZAIDENBERG

Authors
  1. TAKASHI KISHIMOTO
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  2. YURI PROKHOROV
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  3. MIKHAIL ZAIDENBERG
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Correspondence to TAKASHI KISHIMOTO.

Additional information

(TAKASHI KISHIMOTO) Partially supported by a Grant-in-Aid for Scientific Research of JSPS, No. 24740003.

(YURI PROKHOROV) Partially supported by RFBR grant No. 11-01-00336-a, the grant of Leading Scientific Schools No. 4713.2010.1, Simons-IUM fellowship, and AG Laboratory SU-HSE, RF government grant ag. 11.G34.31.0023.

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KISHIMOTO, T., PROKHOROV, Y. & ZAIDENBERG, M. 𝔾a-ACTIONS ON AFFINE CONES. Transformation Groups 18, 1137–1153 (2013). https://doi.org/10.1007/s00031-013-9246-5

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