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arXiv · 2609.22469

Local monodromy, Behrend function and Hilbert scheme of points on $\mathbb{C}^3$

Yunfeng Jiang
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Abstract

We prove a criteria for the Behrend function values on the Hilbert scheme of $n$-points on $\C^3$ from local monodromy and the Denef--Loeser's Lefschetz trace formula of jet spaces. If the powers two, three, and four of the monodromy is unipotent, it reduces respectively to a Hessian parity formula, a cubic-complement formula, and a quartic formula. This gives a Milnor fiber and monodromy based proof of nonconstancy of the Behrend function on $\Hilb^n(\C^3)$ after Jelisiejew-Kool-Schmiermann.

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BibTeXRIS

Yunfeng Jiang. 2026-09-18. Local monodromy, Behrend function and Hilbert scheme of points on $\mathbb{C}^3$. https://arxiv.org/abs/2609.22469

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