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

• Type: Journal
• Year: 2008
• Where: DCC
• Authors: Jeroen Schillewaert
• Keywords: Ane Spaces, Computer Graphics, DCC 2008, Intersection Numbers, Maximum Non-linear Functions