Characterizations of finite classical polar spaces by intersection numbers with hyperplanes and spaces of codimension 2

Abstract

In this article we show that non-singular quadrics and non-singular Hermitian varieties are completely characterized by their intersection numbers with respect to hyperplanes and spaces of codimension 2. This strongly generalizes a result by Ferri and Tallini [5] and also provides necessary and sufficient conditions for quasi-quadrics (respectively their Hermitian analogues) to be non-singular quadrics (respectively Hermitian varieties).

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Correspondence to Stefaan De Winter.

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De Winter, S., Schillewaert, J. Characterizations of finite classical polar spaces by intersection numbers with hyperplanes and spaces of codimension 2. Combinatorica 30, 25–45 (2010). https://doi.org/10.1007/s00493-010-2441-2

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Mathematics Subject Classification (2000)

  • 05B25
  • 51A50