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

Bradley Dirks; Sebastian Olano; Debaditya Raychaudhury

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arXiv · 2607.25861

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

Bradley Dirks·Sebastian Olano·Debaditya Raychaudhury

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Abstract

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

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Bradley Dirks, Sebastian Olano, Debaditya Raychaudhury. 2026-07-28. A Hodge Theoretic Generalization of $\mathbb{Q}$-Homology Manifolds II: Local Complete Intersections. https://arxiv.org/abs/2607.25861

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