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Article: Embeddings of curves in the plane

TitleEmbeddings of curves in the plane
Authors
Issue Date1999
PublisherAcademic 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?
AbstractLet 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 Identifierhttp://hdl.handle.net/10722/156079
ISSN
2015 Impact Factor: 0.66
2015 SCImago Journal Rankings: 1.165
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorShpilrain, Ven_US
dc.contributor.authorYu, JTen_US
dc.date.accessioned2012-08-08T08:40:19Z-
dc.date.available2012-08-08T08:40:19Z-
dc.date.issued1999en_US
dc.identifier.citationJournal Of Algebra, 1999, v. 217 n. 2, p. 668-678en_US
dc.identifier.issn0021-8693en_US
dc.identifier.urihttp://hdl.handle.net/10722/156079-
dc.description.abstractLet 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.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jalgebraen_US
dc.relation.ispartofJournal of Algebraen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleEmbeddings of curves in the planeen_US
dc.typeArticleen_US
dc.identifier.emailYu, JT:yujt@hku.hken_US
dc.identifier.authorityYu, JT=rp00834en_US
dc.description.naturepostprinten_US
dc.identifier.doi10.1006/jabr.1998.7811-
dc.identifier.scopuseid_2-s2.0-0033565132en_US
dc.identifier.hkuros46975-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0033565132&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume217en_US
dc.identifier.issue2en_US
dc.identifier.spage668en_US
dc.identifier.epage678en_US
dc.identifier.isiWOS:000081612000015-
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridShpilrain, V=6603904879en_US
dc.identifier.scopusauthoridYu, JT=7405530208en_US

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