# Incidences of lines in $P^3$ and the arithmetic genus of curves

@article{Kollar2014IncidencesOL, title={Incidences of lines in \$P^3\$ and the arithmetic genus of curves}, author={J'anos Koll'ar}, journal={arXiv: Algebraic Geometry}, year={2014} }

Guth and Katz proved that, as conjectured by Elekes and Sharir, $m$ lines in 3-space have at most constant times $ m^{3/2}$ intersection points, aside from some obvious counter examples. We give an explicit bound for the constant, using the arithmetic genus of the union of the lines.

## One Citation

### Planar surfaces in positive characteristic

- MathematicsSão Paulo Journal of Mathematical Sciences
- 2015

A planar surface is a surface in three-space in which every tangent line has triple or higher contact with the surface at the point of tangency. We study properties of planar surfaces in positive…

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