We study the change of the minimal degree of a logarithmic derivation of a hyperplane arrangement under the addition or the deletion of a hyperplane and give a number of applications. First, we prove the existence of Tjurina maximal line arrangements in a lot of new situations. Then, starting with Ziegler’s example of a pair of arrangements of \(d=9\) lines with \(n_3=6\) triple points in addition to some double points, having the same combinatorics, but distinct minimal degree of a logarithmic derivation, we construct new examples of such pairs, for any number \(d\ge 9\) of lines, and any number \(n_3\ge 6\) of triple points. Moreover, we show that such examples are not possible for line arrangements having only double and triple points, with \(n_3 \le 5\).

我们研究了在超平面的增加或删除下超平面排列的对数导数最小程度的变化，并给出了许多应用。首先，我们证明在许多新情况下Tjurina最大行排列的存在。然后，以齐格勒的\（d = 9 \）行对的示例为例，该行具有\（n_3 = 6 \）三点除一些双点外，具有相同的组合，但对数导数的最小程度不同，我们针对任意数量的\（d \ ge 9 \）行和任意数量的\（n_3 \ ge 6 \）构造此类对的新示例三分。而且，我们表明，对于仅具有双点和三点且具有\（n_3 \ le 5 \）的线排列，此类示例是不可能的。