Vol. 12, No. 2, 2018

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

Shulim Kaliman

Vol. 12 (2018), No. 2, 227–258

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.

Dedicated to my teachers, Vladimir Yakovlevich Lin and Evgeniy Alekseevich Gorin

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proper $G_a$-action on affine 4-space
Mathematical Subject Classification 2010
Primary: 14R20
Secondary: 14L30, 32M17
Received: 11 August 2015
Revised: 18 November 2016
Accepted: 9 August 2017
Published: 13 May 2018
Shulim Kaliman
Department of Mathematics
University of Miami
Coral Gables, FL
United States