On the intersection of Hermitian curves and of Hermitian surfaces
Copyright policy )On the intersection of Hermitian curves and of Hermitian surfaces
The intersection of two Hermitian curves of \(\mathrm{PG}(2,q^2)\) was determined by \textit{B. C. Kestenband} in the papers [Geom. Dedicata 11, 107--117 (1981; Zbl 0452.51007) and Geom. Dedicata 13, 101--106 (1982; Zbl 0495.51008)]. In the paper under review, the authors give a new proof of these results. L. Giuzzi has determined the structure of the intersection of two non-degenerate surfaces \(\mathcal{H}\) and \(\mathcal{H}'\) of \(\mathrm{PG}(3,q^2)\), when the Hermitian pencil defined by \(\mathcal{H}\) and \(\mathcal{H}'\) contains at least one degenerate Hermitian surface. The authors give a new proof of Giuzzi's results and also obtain some new results in the open case when all the Hermitian surfaces of the Hermitian pencil are non-degenerate.
Polar geometry, symplectic spaces, orthogonal spaces, Hermitian curve, Combinatorial structures in finite projective spaces, Discrete Mathematics and Combinatorics, Hermitian suface, Hermitian surface, Theoretical Computer Science
Polar geometry, symplectic spaces, orthogonal spaces, Hermitian curve, Combinatorial structures in finite projective spaces, Discrete Mathematics and Combinatorics, Hermitian suface, Hermitian surface, Theoretical Computer Science
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