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- W2801388574 abstract "Using a variation of Seydewitz’s method of projective generation of quadratic cones, we define an algebraic surface of $$mathop {mathrm{PG}}(3,q^n)$$ , called $$sigma $$ -cone, whose $$mathbb {F}_{q^n}$$ -rational points are the union of a line with a set $$mathcal{A}$$ of $$q^{2n}$$ points. If $$q^n=2^{2h+1}, hge 1$$ , and $$sigma $$ is the automorphism of $$mathbb {F}_{q^n}$$ given by $$x mapsto x^{2^h} $$ , then the set $$mathcal{A}$$ is the affine set of the Luneburg spread of $$mathop {mathrm{PG}}(3,q^n)$$ . If $$n=2$$ and $$sigma $$ is the involutory automorphism of $$mathbb {F}_{q^2}$$ , then a $$sigma $$ -cone is a subset of a Hermitian cone and the set $$mathcal{A}$$ is the union of q non-degenerate Hermitian curves." @default.
- W2801388574 created "2018-05-17" @default.
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- W2801388574 date "2018-04-23" @default.
- W2801388574 modified "2023-09-24" @default.
- W2801388574 title "A generalization of the quadratic cone of $$mathop {mathrm{PG}}(3,q^n)$$ and its relation with the affine set of the Lüneburg spread" @default.
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- W2801388574 doi "https://doi.org/10.1007/s10801-018-0824-4" @default.
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