Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 1, pp. 179-206 (2005)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Constructing non-regular algebraic spreads with asymplecticly complemented regulization

Rolf Riesinger

Patrizigasse 7/14, A--1210 Vienna, Austria

Abstract: We give an application of the second extension of the Thas-Walker construction and exhibit a $4$-parameter family $\cal F$ of explicit examples of spreads of $\mbox{{\rm PG}}(3,\Bbb R)$ with asymplecticly complemented regulization. In $\cal F$ there are symplectic spreads and also asymplectic algebraic spreads. A spread $\cal S$ of $\mbox{{\rm PG}}(3,\Bbb R)$ is called rigid if, apart from the identity, there exists no collineation leaving $\cal S$ invariant; a rigid spread $\cal S$ is said to be hyperrigid if there exists no duality leaving $\cal S$ invariant. The family $\cal F$ contains hyperrigid algebraic spreads as well as rigid algebraic spreads which are not hyperrigid.

Keywords: spread, algebraic spread, hyperrigid spread, $4$-dimensional translation plane

Classification (MSC2000): 51A40, 51H10, 51M30

Full text of the article:

Electronic version published on: 11 Mar 2005. This page was last modified: 4 May 2006.

© 2005 Heldermann Verlag
© 2005--2006 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition