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 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.

This paper has been withdrawn by the author. The paper will be superseded by subsequent article

References in corpus (1)

• Homaloidal hypersurfaces and hypersurfaces with vanishing Hessian