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Pré-Publication, Document De Travail Année : 2017

Equivariant extensions of Ga-torsors over punctured surfaces

Résumé

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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Dates et versions

hal-01569445 , version 1 (26-07-2017)

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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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