On a question of Bourgain about geometric incidences

Details On a question of Bourgain about geometric incidences On a question of Bourgain about geometric incidences

2007-01-14

arxiv.org/abs/math/0701392v1

Mathematics

Combinatorics

7 pages

Scientific paper

Given a set of $s$ points and a set of $n^2$ lines in three-dimensional
Euclidean space such that each line is incident the $n$ points but no $n$ lines
are coplanar, then we have $s=\Omega(n^{11/4})$. This is the first nontrivial
answer to a question recently posed by Jean Bourgain.

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