On Frobenius incidence varieties of linear subspaces over finite fields
Algebraic Geometry
2011-10-20 v4
Abstract
We define Frobenius incidence varieties by means of the incidence relation of Frobenius images of linear subspaces in a fixed vector space over a finite field, and investigate their properties such as supersingularity, Betti numbers and unirationality. These varieties are variants of the Deligne-Lusztig varieties. We then study the lattices associated with algebraic cycles on them. We obtain a positive-definite lattice of rank 84 that yields a dense sphere packing from a 4-dimensional Frobenius incidence variety in characteristic 2.
Keywords
Cite
@article{arxiv.1007.4614,
title = {On Frobenius incidence varieties of linear subspaces over finite fields},
author = {Ichiro Shimada},
journal= {arXiv preprint arXiv:1007.4614},
year = {2011}
}
Comments
24 pages, no figures; Introduction is changed. New references are added