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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 applications, we prove the Strong Monodromy Conjecture and its multivariate generalisation for hyperplane arrangements. Along the way, we confirm both the n/d-conjecture of Budur--Mustaţă--Teitler and its multivariate form due to Budur.

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Cite

BibTeXRIS
BibTeX
@misc{davis2026multivariate,
  title = {{Multivariate V-filtrations and the Strong Monodromy Conjecture for hyperplane arrangements}},
  author = {Dougal Davis and Ruijie Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.25314},
  eprint = {2605.25314},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.25314},
}
RIS
TY  - UNPB
TI  - Multivariate V-filtrations and the Strong Monodromy Conjecture for hyperplane arrangements
AU  - Dougal Davis
AU  - Ruijie Yang
PY  - 2026
DA  - 2026/09/19
PB  - arXiv
DO  - 10.48550/arxiv.2605.25314
UR  - https://arxiv.org/abs/2605.25314
AB  - 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 applications, we prove the Strong Monodromy Conjecture and its multivariate generalisation for hyperplane arrangements. Along the way, we confirm both the n/d-conjecture of Budur--Mustaţă--Teitler and its multivariate form due to Budur.
ER  -