Algebra & Number Theory

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

Shulim Kaliman

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1527040843

Digital Object Identifier
doi:10.2140/ant.2018.12.227

Mathematical Reviews number (MathSciNet)
MR3803702

Zentralblatt MATH identifier
06880887

Subjects
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

Keywords
proper $G_a$-action on affine 4-space

Citation

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. https://projecteuclid.org/euclid.ant/1527040843


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