Free C+-actions on C3 are translations

Shulim Kaliman

doi:10.1007/s00222-003-0336-1

Free C₊-actions on C³ are translations

Shulim Kaliman

Mathematics

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Abstract

Let X be a smooth contractible three-dimensional affine algebraic variety with a free algebraic C₊-action on it such that S = X//C₊ is smooth. We prove that X is isomorphic to S × C and the action is induced by a translation on the second factor. As a consequence we show that any free algebraic C₊-action on C³ is a translation in a suitable coordinate system.

Original language	English (US)
Pages (from-to)	163-173
Number of pages	11
Journal	Inventiones Mathematicae
Volume	156
Issue number	1
DOIs	https://doi.org/10.1007/s00222-003-0336-1
State	Published - Jan 1 2004

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Mathematics(all)

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10.1007/s00222-003-0336-1

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abstract = "Let X be a smooth contractible three-dimensional affine algebraic variety with a free algebraic C+-action on it such that S = X//C+ is smooth. We prove that X is isomorphic to S × C and the action is induced by a translation on the second factor. As a consequence we show that any free algebraic C+-action on C3 is a translation in a suitable coordinate system.",

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AB - Let X be a smooth contractible three-dimensional affine algebraic variety with a free algebraic C+-action on it such that S = X//C+ is smooth. We prove that X is isomorphic to S × C and the action is induced by a translation on the second factor. As a consequence we show that any free algebraic C+-action on C3 is a translation in a suitable coordinate system.

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Free C₊-actions on C³ are translations

Abstract

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