论文信息 - Ovoids with a pencil of translation ovals

Ovoids with a pencil of translation ovals

We show that if an ovoid of PG(3, q), where q>2 is even, has a pencil of translation ovals and if the carrier of the pencil is not an axis of at least one of the ovals in the pencil, then the ovoid is a Tits ovoid. It follows, as a corollary of this and a result of Penttila and Praeger, that if an ovoid of PG(3, q), where q>2 is even, has a pencil of translation ovals then the ovoid is either an elliptic quadric or a Tits ovoid.

Tim Penttila | Christine M. O'Keefe

[1] J. Hirschfeld. Finite projective spaces of three dimensions , 1986 .

[2] B. Segre. On complete caps and ovaloids in three-dimensional Galois spaces of characteristic two , 1959 .

[3] Cheryl E. Praeger,et al. Ovoids and monomial ovals , 1996 .

[4] Tim Penttila,et al. Ovoids ofPG(3, 16) are elliptic quadrics, II , 1990 .

[5] David G. Glynn,et al. Two new sequences of ovals in finite desarguesian planes of even order , 1983 .

[6] G. Panella. Caratterizzazione delle quadriche di uno spazio (tridimensionale) lineare sopra un corpo finito. , 1955 .

[7] J. Hirschfeld. Projective Geometries Over Finite Fields , 1980 .

[8] G. Royle,et al. Classification of ovoids inPG(3, 32) , 1994 .

[9] A. Barlotti,et al. Some topics in finite geometrical structures , 1965 .

[10] Cheryl E. Praeger,et al. Ovoids and Translation Ovals , 1997 .

[11] Michael Walker,et al. A note on the Hering type of inversive planes of even order , 1977 .