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Algebraic density property of Danilov–Gizatullin surfaces

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A Danilov–Gizatullin surface is an affine surface V which is the complement of an ample section S for the ruling of a Hirzebruch surface. The remarkable theorem of Danilov and Gizatullin states that the isomorphism class of V depends only on the self-intersection number (S.S). In this paper we apply the theorem of Danilov–Gizatullin to prove that the Lie algebra generated by the complete algebraic vector fields on V coincides with the set of all algebraic vector fields of V.

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  1. Institute of Mathematical Sciences, Stony Brook University, Stony Brook, NY, 11794, USA

    Fabrizio Donzelli

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  1. Fabrizio Donzelli
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Correspondence to Fabrizio Donzelli.

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Donzelli, F. Algebraic density property of Danilov–Gizatullin surfaces. Math. Z. 272, 1187–1194 (2012). https://doi.org/10.1007/s00209-012-0982-3

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  • DOI: https://doi.org/10.1007/s00209-012-0982-3

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