Geodesic
ℂ*-actions on ℂ³ are linearizable
Kaliman, S.1 ; Koras, M.2 ; Makar-Limanov, L.3 ; Russell, P.4
1 Department of Mathematics & Computer Science, University of Miami, Coral Gables, FL 33124
2 Institute of Mathematics, Warsaw University, Ul. Banacha 2, Warsaw, Poland
3 Department of Mathematics & Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel, and Department of Mathematics, Wayne State University, Detroit, MI 48202
4 Department of Mathematics & Statistics, McGill University, Montreal, QC, Canada, and Centre Interuniversitaire, en Calcul Mathématique, Algébrique (CICMA)
Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 63-71 Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

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.
DOI : 10.1090/S1079-6762-97-00025-5

Kaliman, S. 1 ; Koras, M. 2 ; Makar-Limanov, L. 3 ; Russell, P. 4

1 Department of Mathematics & Computer Science, University of Miami, Coral Gables, FL 33124
2 Institute of Mathematics, Warsaw University, Ul. Banacha 2, Warsaw, Poland
3 Department of Mathematics & Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel, and Department of Mathematics, Wayne State University, Detroit, MI 48202
4 Department of Mathematics & Statistics, McGill University, Montreal, QC, Canada, and Centre Interuniversitaire, en Calcul Mathématique, Algébrique (CICMA) 
@article{10_1090_S1079_6762_97_00025_5,
     author = {Kaliman, S. and Koras, M. and Makar-Limanov, L. and Russell, P.},
     title = {\ensuremath{\mathbb{C}}*-actions on {\ensuremath{\mathbb{C}}{\textthreesuperior}} are linearizable},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {63--71},
     year = {1997},
     volume = {03},
     doi = {10.1090/S1079-6762-97-00025-5},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-97-00025-5/}
}
TY  - JOUR
AU  - Kaliman, S.
AU  - Koras, M.
AU  - Makar-Limanov, L.
AU  - Russell, P.
TI  - ℂ*-actions on ℂ³ are linearizable
JO  - Electronic research announcements of the American Mathematical Society
PY  - 1997
SP  - 63
EP  - 71
VL  - 03
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-97-00025-5/
DO  - 10.1090/S1079-6762-97-00025-5
ID  - 10_1090_S1079_6762_97_00025_5
ER  - 
%0 Journal Article
%A Kaliman, S.
%A Koras, M.
%A Makar-Limanov, L.
%A Russell, P.
%T ℂ*-actions on ℂ³ are linearizable
%J Electronic research announcements of the American Mathematical Society
%D 1997
%P 63-71
%V 03
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-97-00025-5/
%R 10.1090/S1079-6762-97-00025-5
%F 10_1090_S1079_6762_97_00025_5
Kaliman, S.; Koras, M.; Makar-Limanov, L.; Russell, P. ℂ*-actions on ℂ³ are linearizable. Electronic research announcements of the American Mathematical Society, Tome 03 (1997), pp. 63-71. doi: 10.1090/S1079-6762-97-00025-5

[1] Abhyankar, Shreeram S., Moh, Tzuong Tsieng Embeddings of the line in the plane J. Reine Angew. Math. 1975 148 166

[2] Białynicki-Birula, A. Remarks on the action of an algebraic torus on 𝑘ⁿ Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 1966 177 181

[3] Dimca, Alexandru Singularities and topology of hypersurfaces 1992

[4] Ferrero, Miguel, Lequain, Yves, Nowicki, Andrzej A note on locally nilpotent derivations J. Pure Appl. Algebra 1992 45 50

[5] Koras, Mariusz A characterization of 𝐀²/𝐙ₐ Compositio Math. 1993 241 267

[6] Kobayashi, Ryoichi Uniformization of complex surfaces 1990 313 394

[7] Kambayashi, T., Russell, P. On linearizing algebraic torus actions J. Pure Appl. Algebra 1982 243 250

[8] Kraft, Hanspeter, Popov, Vladimir L. Semisimple group actions on the three-dimensional affine space are linear Comment. Math. Helv. 1985 466 479

[9] Koras, Mariusz, Russell, Peter 𝐺ₘ-actions on 𝐴³ 1986 269 276

[10] Koras, Mariusz, Russell, Peter On linearizing “good” 𝐶*-actions on 𝐶³ 1989 93 102

[11] Miyaoka, Yoichi The maximal number of quotient singularities on surfaces with given numerical invariants Math. Ann. 1984 159 171

[12] Miyanishi, Masayoshi, Tsunoda, Shuichiro Noncomplete algebraic surfaces with logarithmic Kodaira dimension -∞ and with nonconnected boundaries at infinity Japan. J. Math. (N.S.) 1984 195 242

[13] Suzuki, Masakazu Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algébriques de l’espace 𝐶² J. Math. Soc. Japan 1974 241 257

Cité par Sources :