A symplectic spread of a 2n-dimensional vector space V over GF(q) is a set of q^n + 1 totally isotropic n-subspaces inducing a partition of the points of the underlying projective space. The corresponding translation plane is called symplectic. We prove that a translation plane of even order is symplectic if and only if it admits a completely regular line oval. Also, a geometric characterization of completely regular line ovals, related to certain symmetric designs is given. These results give a complete solution to a problem set by W. M. Kantor in apparently different situations.
Symplectic translation planes and line ovals / Maschietti, Antonio. - In: ADVANCES IN GEOMETRY. - ISSN 1615-715X. - STAMPA. - 3:(2003), pp. 123-143.
Symplectic translation planes and line ovals
MASCHIETTI, Antonio
2003
Abstract
A symplectic spread of a 2n-dimensional vector space V over GF(q) is a set of q^n + 1 totally isotropic n-subspaces inducing a partition of the points of the underlying projective space. The corresponding translation plane is called symplectic. We prove that a translation plane of even order is symplectic if and only if it admits a completely regular line oval. Also, a geometric characterization of completely regular line ovals, related to certain symmetric designs is given. These results give a complete solution to a problem set by W. M. Kantor in apparently different situations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
