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Counting higher order tangencies for plane curves

Part of: Discrete geometry

Published online by Cambridge University Press:  26 November 2019

Joshua Zahl
Joshua Zahl*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada, Email: jzahl@math.ubc.ca
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Abstract

We prove that n plane algebraic curves determine O(n(k+2)/(k+1)) points of kth order tangency. This generalizes an earlier result of Ellenberg, Solymosi and Zahl on the number of (first order) tangencies determined by n plane algebraic curves.

MSC classification

Primary: 52C10: Erdős problems and related topics of discrete geometry
Secondary: 52C30: Planar arrangements of lines and pseudolines
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 2 , March 2020 , pp. 310 - 317
Copyright
© Cambridge University Press 2019

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Footnotes

†

Supported by a NSERC Discovery Grant.

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