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arXiv · 1404.4613

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

János Kollár
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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.

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János Kollár. 2014-05-08. Incidences of lines in $P^3$ and the arithmetic genus of curves. https://arxiv.org/abs/1404.4613

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