Rees algebras of additive group actions

Adrien Dubouloz (1) , Isac Hedén (2) , Takashi Kishimoto (3)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 University of Warwick [Coventry]
3 Department of Mathematics, Faculty of Science, Saitama University

We establish basic properties of a sheaf of graded algebras canonically associated to every relative affine scheme $f : X \rightarrow S$ endowed with an action of the additive group scheme $\mathbb{G}_{ a,S}$ over a base scheme or algebraic space $S$, which we call the (relative) Rees algebra of the $\mathbb{G}_{ a,S}$-action. We illustrate these properties on several examples which played important roles in the development of the algebraic theory of locally nilpotent derivations and give some applications to the construction of families of affine threefolds with Ga-actions.

Domaines: Géométrie algébrique [math.AG]

Adrien Dubouloz, Isac Hedén, Takashi Kishimoto. Rees algebras of additive group actions. Mathematische Zeitschrift, 2022, 301, pp.593-626. ⟨10.1007/s00209-021-02926-0⟩. ⟨hal-02163916⟩