Let Q0 be the classical generalized quadrangle of order q = 2n (n ≥ 2) arising from a non-degenerate quadratic form in a 5-dimensional vector space defined over a finite field of order q. We consider the rank two geometry X having as points all the elliptic ovoids of Q0 and as lines the maximal pencils of elliptic ovoids of Q0 pairwise tangent at the same point. We first prove that X is isomorphic to a 2-fold quotient of the affine generalized quadrangle Q Q0, where Q is the classical (q, q2)- generalized quadrangle admitting Q0 as a hyperplane. Further, we classify the cliques in the collinearity graph is either a line of X or it consists of 6 or 4 points of X not contained in any line of X, accordingly as n is odd or even.We count the number of cliques of each type and show that those cliques which are not contained in lines of X arise as subgeometries of Q defined over F2.

Cardinali, I., Sastry, N.S.N. (2016). Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES. MATHEMATICAL SCIENCES, 126(4), 591-612 [10.1007/s12044-016-0311-6].

Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order

Cardinali, Ilaria;
2016-01-01

Abstract

Let Q0 be the classical generalized quadrangle of order q = 2n (n ≥ 2) arising from a non-degenerate quadratic form in a 5-dimensional vector space defined over a finite field of order q. We consider the rank two geometry X having as points all the elliptic ovoids of Q0 and as lines the maximal pencils of elliptic ovoids of Q0 pairwise tangent at the same point. We first prove that X is isomorphic to a 2-fold quotient of the affine generalized quadrangle Q Q0, where Q is the classical (q, q2)- generalized quadrangle admitting Q0 as a hyperplane. Further, we classify the cliques in the collinearity graph is either a line of X or it consists of 6 or 4 points of X not contained in any line of X, accordingly as n is odd or even.We count the number of cliques of each type and show that those cliques which are not contained in lines of X arise as subgeometries of Q defined over F2.
Cardinali, I., Sastry, N.S.N. (2016). Elliptic ovoids and their rosettes in a classical generalized quadrangle of even order. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES. MATHEMATICAL SCIENCES, 126(4), 591-612 [10.1007/s12044-016-0311-6].
File in questo prodotto:
File Dimensione Formato  
CARDINALI-NARASIMHASASTRY2016_Article_EllipticOvoidsAndTheirRosettes.pdf

non disponibili

Tipologia: PDF editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 938.18 kB
Formato Adobe PDF
938.18 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1003459