We introduce the notion of subquadrangle regular system of a generalized quadrangle. A subquadrangle regular system of order m on a generalized quadrangle of order (s, t) is a set of embedded subquadrangles with the property that every point lies on exactly m subquadrangles of R. If m is one half of the total number of subquadrangles on a point, we call R a subquadrangle hemisystem. We construct two infinite families of symplectic subquadrangle hemisystems of the Hermitian surface âï(3, q2), q odd, and two infinite families of symplectic subquadrangle hemisystems of 3(q2), q even. Some sporadic examples of symplectic subquadrangle regular systems of âï H(3, q2) are also presented.
Subquadrangle m-regular systems on generalized quadrangles
COSSIDENTE, Antonio;
2011-01-01
Abstract
We introduce the notion of subquadrangle regular system of a generalized quadrangle. A subquadrangle regular system of order m on a generalized quadrangle of order (s, t) is a set of embedded subquadrangles with the property that every point lies on exactly m subquadrangles of R. If m is one half of the total number of subquadrangles on a point, we call R a subquadrangle hemisystem. We construct two infinite families of symplectic subquadrangle hemisystems of the Hermitian surface âï(3, q2), q odd, and two infinite families of symplectic subquadrangle hemisystems of 3(q2), q even. Some sporadic examples of symplectic subquadrangle regular systems of âï H(3, q2) are also presented.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
