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

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

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

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/s00222-003-0336-1

Fingerprint Dive into the research topics of 'Free C<sub>+</sub>-actions on C<sup>3</sup> are translations'. Together they form a unique fingerprint.

Cite this

@article{671de8aa8f8b4026b0c876764e0e916a,

title = "Free C+-actions on C3 are translations",

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.",

author = "Shulim Kaliman",

year = "2004",

month = jan,

day = "1",

doi = "10.1007/s00222-003-0336-1",

language = "English (US)",

volume = "156",

pages = "163--173",

journal = "Inventiones Mathematicae",

issn = "0020-9910",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Free C+-actions on C3 are translations

AU - Kaliman, Shulim

PY - 2004/1/1

Y1 - 2004/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=1842538712&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842538712&partnerID=8YFLogxK

U2 - 10.1007/s00222-003-0336-1

DO - 10.1007/s00222-003-0336-1

M3 - Article

AN - SCOPUS:1842538712

VL - 156

SP - 163

EP - 173

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 1

ER -