Szemerédi-Trotter-type theorems in dimension 3

János Kollár

doi:10.1016/j.aim.2014.11.014

Szemerédi-Trotter-type theorems in dimension 3

János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

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.

Original language	English (US)
Pages (from-to)	30-61
Number of pages	32
Journal	Advances in Mathematics
Volume	271
DOIs	https://doi.org/10.1016/j.aim.2014.11.014
State	Published - Feb 5 2015

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Arithmetic genus
Incidences of lines and points
Szemerédi-Trotter theorem

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10.1016/j.aim.2014.11.014

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title = "Szemer{\'e}di-Trotter-type theorems in dimension 3",

abstract = "We estimate the number of incidences in a configuration of m lines and n points in dimension 3. The main term is mn1/3 if we work over the real or complex numbers but mn2/5 over finite fields.",

keywords = "Arithmetic genus, Incidences of lines and points, Szemer{\'e}di-Trotter theorem",

author = "J{\'a}nos Koll{\'a}r",

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year = "2015",

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doi = "10.1016/j.aim.2014.11.014",

language = "English (US)",

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AU - Kollár, János

PY - 2015/2/5

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N2 - We estimate the number of incidences in a configuration of m lines and n points in dimension 3. The main term is mn1/3 if we work over the real or complex numbers but mn2/5 over finite fields.

AB - We estimate the number of incidences in a configuration of m lines and n points in dimension 3. The main term is mn1/3 if we work over the real or complex numbers but mn2/5 over finite fields.

KW - Arithmetic genus

KW - Incidences of lines and points

KW - Szemerédi-Trotter theorem

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Szemerédi-Trotter-type theorems in dimension 3

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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