Abstract The Hirzebruch–Milnor class is given by the difference between the homology Hirzebruch characteristic class and the virtual one. It is known that the Hirzebruch–Milnor class for a certain singular hypersurface can be calculated by using the Steenbrink spectrum of the local defining function at a point in each stratum of singular locus. Thus far there is no explicit calculation of this invariant for hyperplane arrangements, and we calculate this invariant by two different ways for low dimensional hyperplane arrangements. Finally, we carry out a combinatorial study of the coincidence of the two computations.

中文翻译：

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关于某些低维超平面排列的 Hirzebruch-Milnor 类的显式计算和一些组合

摘要 Hirzebruch-Milnor 类是由同源 Hirzebruch 特征类和虚拟类之间的差异给出的。已知对于某个奇异超曲面的 Hirzebruch-Milnor 类可以通过使用奇异轨迹每个层中一点的局部定义函数的 Steenbrink 谱来计算。到目前为止，还没有明确计算超平面排列的这个不变量，我们通过两种不同的方式计算低维超平面排列的这个不变量。最后，我们对两种计算的重合进行了组合研究。