$\mathbb {C}^*$-actions on $\mathbb {C}^3$ are linearizable
Authors:
S. Kaliman, M. Koras, L. Makar-Limanov and P. Russell
Journal:
Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 63-71
MSC (1991):
Primary 14L30
DOI:
https://doi.org/10.1090/S1079-6762-97-00025-5
Published electronically:
July 31, 1997
MathSciNet review:
1464577
Full-text PDF Free Access
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Abstract: We give the outline of the proof of the linearization conjecture: every algebraic $\mathbb {C}^*$-action on $\mathbb {C}^3$ is linear in a suitable coordinate system.
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- R. Kobayashi, Uniformization of complex surfaces, Adv. Stud. Pure Math. 18 (1990), 313–394.
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- M. Koras and P. Russell, Contractible threefolds and $\mathbb {C}^*$-actions on $\mathbb {C}^3$, CICMA reports 1995-04, to appear in J. Alg. Geometry.
- M. Koras and P. Russell, Actions on $\mathbb {C}^3$: the smooth locus is not of hyperbolic type, CICMA reports, 1996-06.
- Y. Miyaoka, The maximal number of quotient singularities on surfaces with given numerical invariants, Math. Ann. 26 (1984), 159–171.
- L. Makar-Limanov, On the hypersurface $x+x^2y+z^2+t^3=0$ in $\mathbb {C}^4$, Israel Math. J. 96 (1996), 419–429.
- L. Makar-Limanov, Facts about cancellation, preprint, 1996.
- M. Miyanishi, S. Tsunoda, Noncomplete algebraic surfaces with logarithmic Kodaira dimension $-\infty$ and with nonconnected boundaries at infinity, Japan J. Math 10 (1984), 195–242.
- V. Popov, Algebraic actions of connected reductive groups on $\mathbb {A}^3$ are linearizable, preprint, 1996.
- M. Suzuki, Propriétés topologiques des polynomes de deux variables complexes et automorphismes algébriques de l’espace $\mathbb {C}^2$, J. Math. Soc. Japan 26 (1974), 241–257.
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Additional Information
S. Kaliman
Affiliation:
Department of Mathematics & Computer Science, University of Miami, Coral Gables, FL 33124
MR Author ID:
97125
Email:
kaliman@paris-gw.cs.miami.edu
M. Koras
Affiliation:
Institute of Mathematics, Warsaw University, Ul. Banacha 2, Warsaw, Poland
Email:
koras@mimuw.edu.pl
L. Makar-Limanov
Affiliation:
Department of Mathematics & Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel, and Department of Mathematics, Wayne State University, Detroit, MI 48202
Email:
lml@bimacs.cs.biu.ac.il; lml@math.wayne.edu
P. Russell
Affiliation:
Department of Mathematics & Statistics, McGill University, Montreal, QC, Canada, and Centre Interuniversitaire, en Calcul Mathématique, Algébrique (CICMA)
Email:
russell@Math.McGill.CA
Received by editor(s):
March 5, 1997
Published electronically:
July 31, 1997
Additional Notes:
The first author was partially supported by an NSA grant
Communicated by:
Hyman Bass
Article copyright:
© Copyright 1997
American Mathematical Society
