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.

中文翻译：

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计算平面曲线的高阶切线

我们证明n平面代数曲线确定○(n(ķ+2)/(ķ+1)) 点ķ阶相切。这概括了 Ellenberg、Solymosi 和 Zahl 关于（一阶）切线数量的早期结果n平面代数曲线。