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http://dx.doi.org/10.7468/jksmeb.2016.23.3.309

PLANE CURVES MEETING AT A POINT WITH HIGH INTERSECTION MULTIPLICITY  

KIM, SEON JEONG (DEPARTMENT OF MATHEMATICS AND RINS, GYEONGSANG NATIONAL UNIVERSITY)
KANG, EUNJU (BDEPARTMENT OF INFORMATION AND COMMUNICATION ENGINEERING, HONAM UNIVERSITY)
Publication Information
The Pure and Applied Mathematics / v.23, no.3, 2016 , pp. 309-317 More about this Journal
Abstract
As a generalization of an inflection point, we consider a point P on a smooth plane curve C of degree m at which another curve C' of degree n meets C with high intersection multiplicity. Especially, we deal with the existence of two curves of degree m and n meeting at the unique point.
Keywords
intersection multiplicy; intersection number; plane curve;
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  • Reference
1 M. Namba: Families of meromorphic functions on compact Riemann surfaces. Lecture Notes in Math. 767, Springer-Verlag, Berlin, 1979.
2 E. Arbarello, M. Cornalba, P.A. Griffiths & J. Harris: Geometry of Algebraic Curves, I. Springer-Verlag, Berlin/New York, 1985.
3 B. Brieskorn & H. Knörrer: Plane Algebraic Curves. Modern Birkhäuser Classics, Springer Basel, 2012.
4 M. Coppens: The existence of base point free linear systems on smooth plane curves. Journal of Algebraic Geometry 4 (1995), 1-15.
5 J.G. Semple & L. Roth: Introduction to Algebraic Geometry. Oxford University Press, 1985.