Higher Du Bois and higher rational singularities of hypersurfaces
Algebraic Geometry
2024-12-13 v4
Abstract
In this note, we give several equivalent characterizations of higher Du Bois and higher rational singularities in the context of globally defined hypersurfaces. As a key input, we characterize these singularities using the Hodge filtration on the vanishing cycle mixed Hodge module. As an application, we indicate a homological criterion for detecting higher Du Bois and higher rational hypersurface singularities, formulated in terms of the spectral Hirzebruch-Milnor characteristic classes.
Keywords
Cite
@article{arxiv.2301.09084,
title = {Higher Du Bois and higher rational singularities of hypersurfaces},
author = {Laurenţiu Maxim and Ruijie Yang},
journal= {arXiv preprint arXiv:2301.09084},
year = {2024}
}
Comments
v3: Title changed, references added and exposition reorganized; v2: convention of vanishing cycle mixed Hodge module is changed and the proof of Lemma 3.13 is rewritten; v1: 18 pages, comments are welcome!