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We study the change of the minimal degree of a logarithmic derivation of ahyperplane arrangement under the addition or the deletion of a hyperplane, andgive a number of applications. First, we prove the existence of Tjurina maximalline arrangements in a lot of new situations. Then, starting with Ziegler'sexample of a pair of arrangements of $d=9$ lines with $n_3=6$ triple points inaddition to some double points, having the same combinatorics, but distinctminimal degree of a logarithmic derivation, we construct new examples of suchpairs, for any number $d\geq 9$ of lines, and any number $n_3\geq 6$ of triplepoints. Moreover, we show that such examples are not possible for linearrangements having only double and triple points, with $n_3 \leq 5$.

Addition-deletion results for the minimal degree of logarithmic derivations of arrangements