Complex algebraic curves. Annuli
| dc.creator | Borodzik, Maciej | |
| dc.creator | Zoladek, Henryk | |
| dc.date | 2007-08-13 | |
| dc.date.accessioned | 2026-07-07T08:23:23Z | |
| dc.date.available | 2026-07-07T08:23:23Z | |
| dc.description | We provide the full classification of algebraic embeddings of $\mathbb{C}^*$ into $\mathbb{C}^2$ satisfying certain regularity condition, which conjecturally holds for all algebraic maps from $\mathbb{C}^*$ into $\mathbb{C}^2$. The resulting list comprises 1 smooth family, 18 discrete families and 4 special cases. Any embedding known to us can be reduced to one of this list by a de Jonquière transform and a suitable change of variables. The classification uses in general tools from previous work "Complex algebraic curves via Poincare--Hopf formula. I. Parametric lines." (Pacific. J. Math. 229 (2007) No. 2, 307--338): we carefully estimate Milnor numbers of singularities that may appear in the embedding of $\mathbb{C}^*$. We use the regularity condition to bound the sum of so--called codimensions of singular points. The detailed discussion of this condition can be found in http://www.mimuw.edu.pl/~mcboro/pliki/artykuly/curv4.pdf | |
| dc.description | 43 pages. This is the full, unabridged version of our article "Complex algebraic curves via Poincare--Hopf formula. II. Annuli". In this version we include all detailed estimates. The TeX file has been prepared using Scientific Workplace | |
| dc.identifier | https://arxiv.org/abs/0708.1661 | |
| dc.identifier | http://arxiv.org/abs/0708.1661 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135976 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H50, 14R05 (Primary); 14H45; 32S05 (Secondary) | |
| dc.title | Complex algebraic curves. Annuli | |
| dc.type | text |