Szemer\'edi--Trotter-type theorems in dimension 3

János Kollár

Szemer\'edi--Trotter-type theorems in dimension 3

Combinatorics 2014-12-05 v3 Algebraic Geometry

Authors: János Kollár

Abstract

We estimate the number of incidences in a configuration of $m$ lines and $n$ points in dimension 3. The main term is $mn^{1/3}$ if we work over the real or complex numbers but $mn^{2/5}$ over finite fields. Both of these are optimal, aside from a multiplicative constant that is at most 5.

Keywords

incidence geometry of points and lines set theory and dimension theory bound

Cite

@article{arxiv.1405.2243,
  title  = {Szemer\'edi--Trotter-type theorems in dimension 3},
  author = {János Kollár},
  journal= {arXiv preprint arXiv:1405.2243},
  year   = {2014}
}

Comments

This paper supersedes arXiv:1404.4613. Version2: references updated and small changes made. arXiv admin note: substantial text overlap with arXiv:1404.4613 Version 3: Many changes and a new section added on ruled surfaces

Szemer\'edi--Trotter-type theorems in dimension 3

Abstract

Keywords

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