On the explicit calculation of Hirzebruch-Milnor classes of hyperplane arrangements

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 Hodge spectrum of each stratum of singular locus. So far there is no explicit calculation of this invariant for any non-trivial examples, and we calculate this invariant by two different ways for low dimmensional hyperplane arrangements.