Furstenberg sets and Furstenberg schemes over finite fields
Algebraic Geometry
2016-10-05 v1 Classical Analysis and ODEs
Combinatorics
Abstract
We give a lower bound for the size of a subset of containing a rich k-plane in every direction, a k-plane Furstenberg set. The chief novelty of our method is that we use arguments on non-reduced subschemes and flat families to derive combinatorial facts about incidences between points and k-planes in space.
Cite
@article{arxiv.1502.03736,
title = {Furstenberg sets and Furstenberg schemes over finite fields},
author = {Jordan S. Ellenberg and Daniel Erman},
journal= {arXiv preprint arXiv:1502.03736},
year = {2016}
}
Comments
16 pages