Blocking sets of secant and tangent lines with respect to a quadric of $$\text{ PG }(n,q)$$

Abstract

For a set \({\mathcal {L}}\) of lines of \(\text{ PG }(n,q)\), a set X of points of \(\text{ PG }(n,q)\) is called an \({\mathcal {L}}\)-blocking set if each line of \({\mathcal {L}}\) contains at least one point of X. Consider a possibly singular quadric Q of \(\text{ PG }(n,q)\) and denote by \({\mathcal {S}}\) (respectively, \({\mathcal {T}}\)) the set of all lines of \(\text{ PG }(n,q)\) meeting Q in 2 (respectively, 1 or \(q+1\)) points. For \({\mathcal {L}}\in \{{\mathcal {S}},{\mathcal {T}}\cup {\mathcal {S}}\}\), we find the minimal cardinality of an \({\mathcal {L}}\)-blocking set of \(\text{ PG }(n,q)\) and determine all \({\mathcal {L}}\)-blocking sets of that minimal cardinality.