Algebra & Number Theory

Proper $G_a$-actions on $\mathbb{C}^4$ preserving a coordinate

Shulim Kaliman

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We prove that the actions mentioned in the title are translations. We show also that for certain Ga-actions on affine fourfolds the categorical quotient of the action is automatically an affine algebraic variety and describe the geometric structure of such quotients.

Article information

Algebra Number Theory, Volume 12, Number 2 (2018), 227-258.

Received: 11 August 2015
Revised: 18 November 2016
Accepted: 9 August 2017
First available in Project Euclid: 23 May 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14R20: Group actions on affine varieties [See also 13A50, 14L30]
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17] 32M17: Automorphism groups of Cn and affine manifolds

proper $G_a$-action on affine 4-space


Kaliman, Shulim. Proper $G_a$-actions on $\mathbb{C}^4$ preserving a coordinate. Algebra Number Theory 12 (2018), no. 2, 227--258. doi:10.2140/ant.2018.12.227.

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