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Article: Embeddings of curves in the plane
Title | Embeddings of curves in the plane |
---|---|
Authors | |
Issue Date | 1999 |
Publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra |
Citation | Journal Of Algebra, 1999, v. 217 n. 2, p. 668-678 How to Cite? |
Abstract | Let K[x,y] be the polynomial algebra in two variables over a field K of characteristic 0. In this paper, we contribute toward a classification of two-variable polynomials by classifying (up to an automorphism of K[x,y]) polynomials of the form axn+bym+∑im+jn≤mncijxiyj, a,b,cij∈K (i.e., 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≥2, there is an irreducible curve with one place at infinity which has at least k equivalent embeddings in C2. 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 {p(x,y)=0} is an irreducible simply connected curve. © 1999 Academic Press. |
Persistent Identifier | http://hdl.handle.net/10722/156079 |
ISSN | 2023 Impact Factor: 0.8 2023 SCImago Journal Rankings: 1.023 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Shpilrain, V | en_US |
dc.contributor.author | Yu, JT | en_US |
dc.date.accessioned | 2012-08-08T08:40:19Z | - |
dc.date.available | 2012-08-08T08:40:19Z | - |
dc.date.issued | 1999 | en_US |
dc.identifier.citation | Journal Of Algebra, 1999, v. 217 n. 2, p. 668-678 | en_US |
dc.identifier.issn | 0021-8693 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/156079 | - |
dc.description.abstract | Let K[x,y] be the polynomial algebra in two variables over a field K of characteristic 0. In this paper, we contribute toward a classification of two-variable polynomials by classifying (up to an automorphism of K[x,y]) polynomials of the form axn+bym+∑im+jn≤mncijxiyj, a,b,cij∈K (i.e., 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≥2, there is an irreducible curve with one place at infinity which has at least k equivalent embeddings in C2. 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 {p(x,y)=0} is an irreducible simply connected curve. © 1999 Academic Press. | en_US |
dc.language | eng | en_US |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebra | en_US |
dc.relation.ispartof | Journal of Algebra | en_US |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.title | Embeddings of curves in the plane | en_US |
dc.type | Article | en_US |
dc.identifier.email | Yu, JT:yujt@hku.hk | en_US |
dc.identifier.authority | Yu, JT=rp00834 | en_US |
dc.description.nature | postprint | en_US |
dc.identifier.doi | 10.1006/jabr.1998.7811 | - |
dc.identifier.scopus | eid_2-s2.0-0033565132 | en_US |
dc.identifier.hkuros | 46975 | - |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0033565132&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 217 | en_US |
dc.identifier.issue | 2 | en_US |
dc.identifier.spage | 668 | en_US |
dc.identifier.epage | 678 | en_US |
dc.identifier.isi | WOS:000081612000015 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Shpilrain, V=6603904879 | en_US |
dc.identifier.scopusauthorid | Yu, JT=7405530208 | en_US |
dc.identifier.issnl | 0021-8693 | - |