A Characterisation of the Generalized Quadrangle Q (5, q) Using Cohomology |
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Authors: | Matthew R Brown |
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Institution: | (1) Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, Gent, B-9000, Belgium |
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Abstract: | If a GQ S of order (s, s) is contained in a GQ S of order (s, s
2) as a subquadrangle, then for each point X of S\S the set of points
of S collinear with X form an ovoid of S. Thas and Payne proved that if S=
(4,q),q even, and
is an elliptic quadric for each XS\S,thenS
(5,q). In this paper we provide a single proof for the q odd and q even cases by establishing a link between the geometry involved and the first cohomology group of a related simplicial complex. |
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Keywords: | generalized quadrangle subquadrangle cohomology ovoid |
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