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

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, Mustaţă, and Teitler, holds for generic multiplicities. Consequently, strong monodromy conjecture holds for hyperplane arrangements with generic multiplicities as well.

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