Embeddings of curves in the plane
| dc.creator | Shpilrain, Vladimir | |
| dc.creator | Yu, Jie-Tai | |
| dc.date | 1998-09-10 | |
| dc.date.accessioned | 2026-07-07T05:25:57Z | |
| dc.date.available | 2026-07-07T05:25:57Z | |
| dc.description | In this paper, we contribute toward a classification of two-variable polynomials by classifying (up to an automorphism of $C^2$) polynomials whose Newton polygon is either a triangle or a line segment. Our classification has several applications to the study of embeddings of algebraic curves in the plane. In particular, we show that for any $k \ge 2$, there is an irreducible curve with one place at infinity, which has at least $k$ inequivalent embeddings in $C^2$. Also, upon combining our method with a well-known theorem of Zaidenberg and Lin, we show that one can decide "almost" just by inspection whether or not a polynomial fiber is an irreducible simply connected curve. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/9809049 | |
| dc.identifier | http://arxiv.org/abs/math/9809049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77377 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14E09, 14E25 | |
| dc.title | Embeddings of curves in the plane | |
| dc.type | text |