# Incidences with curves and surfaces in three dimensions, with applications to distinct and repeated distances

@inproceedings{Sharir2017IncidencesWC, title={Incidences with curves and surfaces in three dimensions, with applications to distinct and repeated distances}, author={M. Sharir and Noam Solomon}, booktitle={SODA}, year={2017} }

We study a wide spectrum of incidence problems involving points and curves or points and surfaces in $\mathbb R^3$. The current (and in fact the only viable) approach to such problems, pioneered by Guth and Katz [2010,2015], requires a variety of tools from algebraic geometry, most notably (i) the polynomial partitioning technique, and (ii) the study of algebraic surfaces that are ruled by lines or, in more recent studies [Guth-Zahl 2016], by algebraic curves of some constant degree. By… Expand

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