A Hodge Theoretic Generalization of $\mathbb{Q}$-Homology Manifolds II: Local Complete Intersections

Recently, the authors introduced and studied a singularity invariant of a complex algebraic variety $Z$, written $\text{HRH}(Z)$ (for ``Hodge rational homology’’ manifold level). In this paper, we focus on local complete intersection subvarieties. We relate $\text{HRH}(Z)$ to various well-known invariants, like Bernstein–Sato polynomials and the Dimca-Maisonobe-Saito spectrum. In the hypersurface case it turns out that $\text{HRH}(Z)$ can be completely characterized by these invariants, though higher codimension case is more subtle.