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Degree complexity bounds on the intersection of algebraic curves

Authors:

S. S. Abhyankar,

S. Chandrasekar,

V. ChandruAuthors Info & Claims

SCG '89: Proceedings of the fifth annual symposium on Computational geometry

Pages 88 - 93

https://doi.org/10.1145/73833.73843

Published: 05 June 1989 Publication History

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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.

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Abhyankar, S.S., Chandrasekar, S. and Chandru, V., "Intersection of Algebraic Space Curves," Technical Report CC- 88-13, I.I.E.S., Purdue University, West Lafayette, IN 47097, April 1988.

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Abhyankar, S.S., Chandrasekar, S. and Chandru, V., "Improper Intersection of Algebraic Curves," Technical Report CC-88-24, I.I.E.S., Purdue University, West Lafayette, IN 47907, September 1988.

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Degree complexity bounds on the intersection of algebraic curves

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Published In

SCG '89: Proceedings of the fifth annual symposium on Computational geometry

June 1989

401 pages

ISBN:0897913183

DOI:10.1145/73833

Chairman:
Kurt Mehlhorn

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 June 1989

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Improper intersection of algebraic curves

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