We introduce the notion of relative subquadrangle regular system of a generalized quadrangle. A relative subquadrangle regular system of order m on a generalized quadrangle S of order (s, t) is a set R of embedded subquadrangles with a prescribed intersection property with respect to a given subquadrangle T such that every point of S T lies on exactly m subquadrangles of R . If m is one half of the total number of such subquadrangles on a point we call R a relative subquadrangle hemisystem with respect to T. We construct two infinite families of symplectic relative subquadrangle hemisystems of the Hermitian surface H(3,q^2) , q even.
Relative symplectic subquadrangle hemisystems of the Hermitian surface
MARINO, Giuseppe;
2014
Abstract
We introduce the notion of relative subquadrangle regular system of a generalized quadrangle. A relative subquadrangle regular system of order m on a generalized quadrangle S of order (s, t) is a set R of embedded subquadrangles with a prescribed intersection property with respect to a given subquadrangle T such that every point of S T lies on exactly m subquadrangles of R . If m is one half of the total number of such subquadrangles on a point we call R a relative subquadrangle hemisystem with respect to T. We construct two infinite families of symplectic relative subquadrangle hemisystems of the Hermitian surface H(3,q^2) , q even.File in questo prodotto:
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