# Rees algebras of additive group actions

Abstract : 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.
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Preprints, Working Papers, ...

Cited literature [32 references]

https://hal.archives-ouvertes.fr/hal-02163916
Submitted on : Monday, June 24, 2019 - 4:39:29 PM
Last modification on : Thursday, June 27, 2019 - 1:49:36 AM

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Rees-Ga-Var.pdf
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### Identifiers

• HAL Id : hal-02163916, version 1
• ARXIV : 1906.11016

### Citation

Adrien Dubouloz, Isac Hedén, Takashi Kishimoto. Rees algebras of additive group actions. 2019. ⟨hal-02163916⟩

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