Counting higher order tangencies for plane curves

Abstract

We prove that $n$ plane algebraic curves determine $O(n^{(k+2)/(k+1)})$ points of $k$-th 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.

8 pages, 0 figures. v2: to appear in Combin. Probab. Comput

References in corpus (1)

• Cutting Algebraic Curves into Pseudo-segments and Applications