Blocking Sets in the complement of hyperplane arrangements in projective space

Abstract: It is well know that the theory of minimal blocking sets is studied by several author. Another theory which is also studied by a large number of researchers is the theory of hyperplane arrangements. We can remark that the affine space $AG(n,q)$ is the complement of the line at infinity in $PG(n,q)$. Then $AG(n,q)$ can be regarded as the complement of an hyperplane arrangement in $PG(n,q)$! Therefore the study of blocking sets in the affine space $AG(n,q)$ is simply the study of blocking sets in the complement of a finite arrangement in $PG(n,q)$. In this paper the author generalizes this remark starting to study the problem of existence of blocking sets in the complement of a given hyperplane arrangement in $PG(n,q)$. As an example she solves the problem for the case of braid arrangement. Moreover she poses significant questions on this new and interesting problem.