Embeddings of curves in the plane

dc.creatorShpilrain, Vladimir
dc.creatorYu, Jie-Tai
dc.date1998-09-10
dc.date.accessioned2026-07-07T05:25:57Z
dc.date.available2026-07-07T05:25:57Z
dc.descriptionIn 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.description11 pages
dc.identifierhttps://arxiv.org/abs/math/9809049
dc.identifierhttp://arxiv.org/abs/math/9809049
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77377
dc.subjectAlgebraic Geometry
dc.subject14E09, 14E25
dc.titleEmbeddings of curves in the plane
dc.typetext

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