Free C+-actions on C3 are translations

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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 languageEnglish (US)
Pages (from-to)163-173
Number of pages11
JournalInventiones Mathematicae
Volume156
Issue number1
DOIs
StatePublished - Jan 1 2004

ASJC Scopus subject areas

  • Mathematics(all)

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