Variation of Archimedean Zeta Function and $n/d$-Conjecture for Generic Multiplicities

Quan Shi; Huaiqing Zuo

Variation of Archimedean Zeta Function and $n/d$-Conjecture for Generic Multiplicities

Algebraic Geometry 2025-02-24 v2

Authors: Quan Shi , Huaiqing Zuo

Abstract

For $f_1,...,f_r\in \mathbb C[z_1,...,z_n]\setminus \mathbb C$ , we introduce the variation of archimedean zeta function. As an application, we show that the $n/d$ -conjecture, proposed by Budur, Musta\c{t}\u{a}, and Teitler, holds for generic multiplicities. Consequently, strong monodromy conjecture holds for hyperplane arrangements with generic multiplicities as well.

Keywords

Archimedean zeta function n/d-conjecture generic multiplicities monodromy conjecture hyperplane arrangements variation

Cite

@article{arxiv.2411.00757,
  title  = {Variation of Archimedean Zeta Function and $n/d$-Conjecture for Generic Multiplicities},
  author = {Quan Shi and Huaiqing Zuo},
  journal= {arXiv preprint arXiv:2411.00757},
  year   = {2025}
}

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v2: more readable now

Variation of Archimedean Zeta Function and $n/d$-Conjecture for Generic Multiplicities

Abstract

Keywords

Cite

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