Equivariant extensions of Ga-torsors over punctured surfaces

Adrien Dubouloz; Isac Hedén; Takashi Kishimoto

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arXiv · 1707.08768

Equivariant extensions of Ga-torsors over punctured surfaces

Adrien Dubouloz·Isac Hedén·Takashi Kishimoto

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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 $\rightarrow$ 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 $\pi$ : X $\rightarrow$ 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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Adrien Dubouloz, Isac Hedén, Takashi Kishimoto. 2017-07-27. Equivariant extensions of Ga-torsors over punctured surfaces. https://arxiv.org/abs/1707.08768

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