A characterization of quadrics by intersection numbers

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A characterization of quadrics by intersection numbers
This work is inspired by a paper of Hertel and Pott on maximum non-linear functions [8]. Geometrically, these functions correspond with quasi-quadrics; objects introduced in [5]. Hertel and Pott obtain a characterization of some binary quasi-quadrics in ane spaces by their intersection numbers with hyperplanes and spaces of codimension 2. We obtain a similar characterization for quadrics in projective spaces by intersection numbers with low-dimensional spaces. Ferri and Tallini [7] characterized the non-singular quadric Q(4; q) by its intersection numbers with planes and solids. We prove a corollary of this theorem for Q(4; q) and then extend this corollary to all quadrics in P G(n; q); n 4. The only exceptions we get occur for q even, where we can have an oval or an ovoid as intersection with our point set in the non-singular part. 1 Notations and background
Jeroen Schillewaert
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where DCC
Authors Jeroen Schillewaert
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