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Article Dans Une Revue Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Année : 2020

Equivariant extensions of $\mathbb{G}_a$-torsors over punctured surfaces

Résumé

Motivated by the study of the structure of algebraic actions of the additive group on affine threefolds X, we consider a special class of such varieties whose algebraic quotient morphisms X -> X//G(a) 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 G(a)-actions, whose algebraic quotient morphisms pi : X -> X//G(a) 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-03280672 , version 1 (07-07-2021)

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Citer

Adrien Dubouloz, Isac Hedén, Takashi Kishimoto. Equivariant extensions of $\mathbb{G}_a$-torsors over punctured surfaces. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2020, 21 (SI), pp.133-167. ⟨10.2422/2036-2145.201710_002⟩. ⟨hal-03280672⟩
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