Tohoku Mathematical Journal

Lifting of the additive group scheme actions

Kayo Masuda and Masayoshi Miyanishi

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Let $B$ be a normal affine $\boldsymbol{C}$-domain and let $A$ be a $\boldsymbol{C}$-subalgebra of $B$ such that $B$ is a finite $A$-module. Let $\delta$ be a locally nilpotent derivation on $A$. Then $\delta$ lifts uniquely to the quotient field $L$ of $B$, which we denote by $\Delta$. We consider when $\Delta$ is a locally nilpotent derivation of $B$. This is a classical subject treated in [17, 19, 16]. We are interested in the case where $A$ is the $G$-invariant subring of $B$ when a finite group $G$ acts on $B$. As a related topic, we treat in the last section the finite coverings of log affine pseudo-planes in terms of the liftings of the $\boldsymbol{A}^1$-fibrations associated with locally nilpotent derivations.

Article information

Tohoku Math. J. (2), Volume 61, Number 2 (2009), 267-286.

First available in Project Euclid: 24 June 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14R20: Group actions on affine varieties [See also 13A50, 14L30]
Secondary: 14R25: Affine fibrations [See also 14D06]


Masuda, Kayo; Miyanishi, Masayoshi. Lifting of the additive group scheme actions. Tohoku Math. J. (2) 61 (2009), no. 2, 267--286. doi:10.2748/tmj/1245849448.

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