$\mathbb{Q}$-同调流形的霍奇理论推广II：局部完全交
A Hodge Theoretic Generalization of $\mathbb{Q}$-Homology Manifolds II: Local Complete Intersections
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中文总结 AI 辅助
研究复代数簇$Z$的奇点不变量$\HRH(Z)$，聚焦局部完全交子簇，将其与伯恩斯坦 - 佐藤多项式等著名不变量联系，超曲面情形可由这些不变量完全刻画$\HRH(Z)$，高余维情形更复杂。
中文摘要 AI 辅助
最近，作者引入并研究了复代数簇$Z$的一个奇点不变量，记为$\HRH(Z)$（用于“霍奇有理同调”流形层面）。本文聚焦于局部完全交子簇，将$\HRH(Z)$与各种著名不变量联系起来，如伯恩斯坦 - 佐藤多项式和迪姆卡 - 迈松诺贝 - 斋藤谱。在超曲面情形下，$\HRH(Z)$可由这些不变量完全刻画，高余维情形则更微妙。
英文摘要
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.
