On the explicit calculation of Hirzebruch–Milnor classes of certain low dimensional hyperplane arrangements and some combinatorics

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.