A Note on a Specific Pencil of Conics in the Galois Fields of Order 2^n

Details A Note on a Specific Pencil of Conics in the Galois Fields of Order 2^n A Note on a Specific Pencil of Conics in the Galois Fields of Order 2^n

2000-12-21

arxiv.org/abs/math/0012214v1

Mathematics

Algebraic Geometry

2 pages, no figures

Scientific paper

The pencil of conics featuring three degenerate conics each of which is a
line-pair is briefly inspected in a Galois field of characteristic two. It is
shown that if two degenerates are conjugate imaginary line pairs, the third
must be a real line pair; this contradicts Campbell's claim (Campbell 1927)
that all the three singular conics are conjugate imaginary line pairs.

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