Abstract
{\em Quasi-quadrics} were introduced by Penttila, De Clerck, O'Keefe and Hamilton in [2]. They are defined as point sets which have the same intersection numbers with respect to hyperplanes as non-singular quadrics. We extend this definition in two ways. The first extension is to {\em quasi-Hermitian varieties}, which are point sets which have the same intersection numbers with respect to hyperplanes as non-singular Hermitian varieties. The second one is to {\em singular quasi-quadrics}, i.e. point sets $\mathcal{K}$ which have the same intersection numbers with respect to hyperplanes as singular quadrics. Our starting point was to investigate whether every singular quasi-quadric is a cone over a non-singular quasi-quadric. This question is tackled in the case of a point set $\mathcal{K}$ with the same intersection numbers with respect to hyperplanes as a point over an ovoid.
Citation
S. De Winter. J. Schillewaert. "A note on quasi-Hermitian varieties and singular quasi-quadrics." Bull. Belg. Math. Soc. Simon Stevin 17 (5) 911 - 918, december 2010. https://doi.org/10.36045/bbms/1292334065
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