On the minimal value of global Tjurina numbers for line arrangements

Abstract

We show that a general lower bound for the global Tjurina number of a reduced complex projective plane curve, given by Andrew A. du Plessis and Charles T. C. Wall, can be improved when the curve is a line arrangement. This fact is in sharp contrast to a conjecture saying that the general upper bound for the global Tjurina number of a reduced complex projective plane curve, also given by du Plessis and Wall, is realized by line arrangements in practically all cases.