Proper Ga-actions on ℂ4 preserving a coordinate

Kaliman, Shulim

doi:10.2140/ant.2018.12.227

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

Shulim Kaliman

Vol. 12 (2018), No. 2, 227–258

DOI: 10.2140/ant.2018.12.227

Abstract

We prove that the actions mentioned in the title are translations. We show also that for certain $G_{a}$ -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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Keywords

proper $G_a$-action on affine 4-space

Mathematical Subject Classification 2010

Primary: 14R20

Secondary: 14L30, 32M17

Milestones

Received: 11 August 2015

Revised: 18 November 2016

Accepted: 9 August 2017

Published: 13 May 2018

Authors

Shulim Kaliman
Department of Mathematics University of Miami Coral Gables, FL United States

Vol. 12, No. 2, 2018