Covers of {${\rm PG}(3,q)$} and of finite generalized quadrangles | Zendy

Aart Blokhuis | Zendy; Christine M. O’Keefe | Zendy; Stanley E. Payne | Zendy; Leo Storme | Zendy; H.A. Wilbrink | Zendy

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Covers of {${\rm PG}(3,q)$} and of finite generalized quadrangles

Author(s) -

Aart Blokhuis,

Christine M. O’Keefe,

Stanley E. Payne,

Leo Storme,

H.A. Wilbrink

Publication year - 1998

Publication title -

bulletin of the belgian mathematical society - simon stevin

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.36

H-Index - 31

eISSN - 2034-1970

pISSN - 1370-1444

DOI - 10.36045/bbms/1103408998

Subject(s) - cover (algebra) , combinatorics , mathematics , set (abstract data type) , contrast (vision) , geometry , physics , computer science , optics , mechanical engineering , engineering , programming language

This article studies covers in $\PG(3,q)$ and in generalized quadrangles. The excess of a cover is defined to be the difference between the number of lines in the cover and the number of lines in a spread. In contrast with the theory of partial spreads which tells us that large partial spreads can be extended to spreads, in $\PG(3,q)$ and in some generalized quadrangles, there exist minimal covers with small excess. For such minimal covers with small excess, we describe the structure of the set of points lying on at least two lines of the cover.

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