Incidences with Curves in $\mathbb{R}^d$

[摘要] We prove that the number of incidences between $m$ points and $n$ bounded-degree curves with $k$ degrees of freedom in ${\mathbb R}^d$ is\[ O\left(m^{\frac{k}{dk-d+1}+\varepsilon}n^{\frac{dk-d}{dk-d+1}}+ \sum_{j=2}^{d-1} m^{\frac{k}{jk-j+1}+\varepsilon}n^

[学科分类] 离散数学和组合数学

[关键词] Geometic incidences;Discrete geometry;Polynomial partitioning;Polynomial curves