Degree complexity bounds on the intersection of algebraic curves

Authors:
S. S. Abhyankar;S. Chandrasekar;V. Chandru
Affiliations:
Purdue Unviersity, West Lafayette, IN and Departments of Mathematics, Computer Science and Industrial Engineering;Purdue Unviersity, West Lafayette, IN and School of Industrial Engineering;Purdue Unviersity, West Lafayette, IN and School of Industrial Engineering
Venue:
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Year:
1989

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Abstract

The intersection of algebraic curves in three and higher dimensional spaces is considered. An algebrogeometric technique is developed for obtaining an upper bound on the number of intersection points of two irreducible algebraic curves. The asymptotic bounds are shown to be a function of only the degrees of the two intersecting curves. Some specific examples involving curves in 3-space are analyzed.