A characterization of m-ovoids and i-tight sets of polar spaces
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Bart De Bruyn
Abstract
Let P be a finite polar space of rank r ≥ 2 with q + 1 ≥ 3 points on each line. In [J. Bamberg, S. Kelly, M. Law, T. Penttila, Tight sets and m-ovoids of finite polar spaces. J. Combin. Theory Ser. A114 (2007), 1293–1314. MR2353124] and [J. Bamberg, M. Law, T. Penttilla, Tight sets and m-ovoids of generalised quadrangles. Combinatorica, to appear.] it was shown that every m-ovoid of P intersects every i-tight set of P in precisely mi points. In the present paper, we characterize m-ovoids of P as those sets of points which have constant intersection size with each member of a “nice family” of i-tight sets of P and conversely, we characterize i-tight sets of P as those sets of points which have constant intersection size with each member of a “nice family” of m-ovoids. Some interesting corollaries of these characterization theorems are given.
© de Gruyter 2008
Articles in the same Issue
- A rigidity result for domains with a locally strictly convex point
- On the geometry of Grassmannian equivalent connections
- On Lie groups as quasi-Kähler manifolds with Killing Norden metric
- Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold
- A characterization of m-ovoids and i-tight sets of polar spaces
- On Grassmann secant extremal varieties
- Almost del Pezzo manifolds
- Projective models of K3 surfaces with an even set
- Nonrational del Pezzo fibrations
- Principal bundles over a smooth real projective curve of genus zero
Articles in the same Issue
- A rigidity result for domains with a locally strictly convex point
- On the geometry of Grassmannian equivalent connections
- On Lie groups as quasi-Kähler manifolds with Killing Norden metric
- Relating the curvature tensor and the complex Jacobi operator of an almost Hermitian manifold
- A characterization of m-ovoids and i-tight sets of polar spaces
- On Grassmann secant extremal varieties
- Almost del Pezzo manifolds
- Projective models of K3 surfaces with an even set
- Nonrational del Pezzo fibrations
- Principal bundles over a smooth real projective curve of genus zero
