Incidences of lines in P³ and the arithmetic genus of curves

2014/04/16 by Janós Kollár, János Kollár, Kollár, János · 1 citation
Computer Science · Mathematics · #05A20 #14N20 #51E20 #52B55 #52C10 #68R05 #Advanced Graph Theory Research #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Limits and Structures in Graph Theory #math.AG #math.CO #msc:05A20 #msc:14N20 #msc:51E20 #msc:52B55 #msc:52C10 #msc:68R05

paper · pdf · doi:10.48550/arxiv.1404.4613

This paper has been withdrawn by the author. The paper will be superseded by subsequent article

openalex publication_date 2014/04/16 · arxiv created 2014/05/08 · arxiv updated 2014/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Szemerédi--Trotter-type theorems in dimension 3

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