Incidences of lines in $P^3$ and the arithmetic genus of curves
Abstract
Guth and Katz proved that, as conjectured by Elekes and Sharir, $m$ lines in 3space 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2014
 arXiv:
 arXiv:1404.4613
 Bibcode:
 2014arXiv1404.4613K
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics;
 05A20;
 52B55;
 52C10;
 14N20;
 68R05;
 51E20
 EPrint:
 This paper has been withdrawn by the author. The paper will be superseded by subsequent article