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arXiv · 2605.25314

Multivariate V-filtrations and the Strong Monodromy Conjecture for hyperplane arrangements

Dougal Davis·Ruijie Yang
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Abstract

In this work, we develop a new theory of multivariate V-filtration on D-modules along a simple normal crossing divisor and relate it with Sabbah's multi-filtration. We establish several new structural results and relate them with the Hodge filtration on free-monodromic local systems from geometric representation theory. As an illustrative application, we give a conceptual and very quick proof of the Strong Monodromy Conjecture and its multivariate generalisation for hyperplane arrangements. Along the way, we confirm both the n/d-conjecture of Budur--Musta\c{t}\u{a}--Teitler and its multivariate form due to Budur.

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Dougal Davis, Ruijie Yang. 2026-05-25. Multivariate V-filtrations and the Strong Monodromy Conjecture for hyperplane arrangements. https://arxiv.org/abs/2605.25314

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