Examples of Hirzebruch-Milnor classes of projective hypersurfaces detecting higher du Bois or rational singularities

TL;DR

This paper explores how Hirzebruch-Milnor classes of projective hypersurfaces can be used to identify higher du Bois or rational singularities, with specific focus on particular cases and clarifications of previous work.

Contribution

It demonstrates the limited applicability of Hirzebruch-Milnor classes for detecting certain singularities and clarifies aspects of earlier research.

Findings

Hirzebruch-Milnor classes can detect higher du Bois or rational singularities in specific cases.

The paper provides clarifications on previous results and methods.

Detection of singularities using these classes is not universally applicable.

Abstract

We show that it is possible to utilize the Hirzebruch-Milnor classes of projective hypersurfaces in the classical sense to detect higher du Bois or rational singularities only in some special cases. We also give several remarks clarifying some points in my earlier papers.