401 research outputs found
On Frobenius incidence varieties of linear subspaces over finite fields
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.Comment: 24 pages, no figures; Introduction is changed. New references are
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