On Frobenius incidence varieties of linear subspaces over finite fields

Details On Frobenius incidence varieties of linear subspaces over finite fields On Frobenius incidence varieties of linear subspaces over finite fields

2010-07-27

arxiv.org/abs/1007.4614v4

Mathematics

Algebraic Geometry

24 pages, no figures; Introduction is changed. New references are added

Scientific paper

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.

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