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

TL;DR

This paper explicitly calculates the Hirzebruch-Milnor classes for low-dimensional hyperplane arrangements, providing new methods to evaluate this invariant for specific singular hypersurfaces.

Contribution

It introduces two different approaches to explicitly compute Hirzebruch-Milnor classes for hyperplane arrangements, filling a gap in practical calculations.

Findings

Explicit formulas for low-dimensional cases

Comparison of two computational methods

New insights into singular hypersurface invariants

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.