CHARACTERIZATIONS OF FINITE CLASSICALPOLAR SPACES BY INTERSECTION NUMBERSWITH HYPERPLANES AND SPACES OF CODIMENSION 2

摘要

In this article we show that non-singular quadrics and non-singular Hermitian varietiesare completely characterized by their intersection numbers with respect to hyperplanesand 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 theirHermitian analogues) to be non-singular quadrics (respectively Hermitian varieties).