• Corpus ID: 119136896

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

  title={Incidences of lines in \$P^3\$ and the arithmetic genus of curves},
  author={J'anos Koll'ar},
  journal={arXiv: Algebraic Geometry},
  • J. Koll'ar
  • Published 16 April 2014
  • Mathematics
  • arXiv: Algebraic Geometry
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. 
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