Equivariant extensions of Ga-torsors over punctured surfaces

Abstract : Motivated by the study of the structure of algebraic actions the additive group on affine threefolds X, we consider a special class of such varieties whose algebraic quotient morphisms X → X//Ga restrict to principal homogeneous bundles over the complement of a smooth point of the quotient. We establish basic general properties of these varieties and construct families of examples illustrating their rich geometry. In particular, we give a complete classification of a natural subclass consisting of threefolds X endowed with proper Ga-actions, whose algebraic quotient morphisms π : X → X//Ga are surjective with only isolated degenerate fibers, all isomorphic to the affine plane A 2 when equipped with their reduced structures.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01569445
Contributeur : Adrien Dubouloz <>
Soumis le : mercredi 26 juillet 2017 - 17:23:15
Dernière modification le : vendredi 28 juillet 2017 - 15:13:44

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  • HAL Id : hal-01569445, version 1
  • ARXIV : 1707.08768

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Adrien Dubouloz, Isac Hedén, Takashi Kishimoto. Equivariant extensions of Ga-torsors over punctured surfaces. 2017. 〈hal-01569445〉

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