Generalized cotangency sets in projective spaces (Q2714347)

Let \(P=PG(n,F)\) be the \(n\)-dimensional projective space over the commutative field \(F\). In the case \(n=2\) the cotangency set was defined by \textit{A. A. Bruen} and \textit{J. C. Fisher} [Discrete Math. 106/107, 93-96 (1992; Zbl 0761.51007)]. In this paper the author defines \(k\)-cotangency set for \(2\leq k\leq n\). NEWLINENEWLINENEWLINEThe main theorem is the following: If \(S\) is a proper \(n\)-cotangency set in an \(n\)-dimensional space, then \(S\) does not contain \(n+2\) points in general position. NEWLINENEWLINENEWLINESome applications about quadrics and Hermitian varieties are given as consequences of the properties of cotangency sets.