Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Davis, Dougal, Yang, Ruijie
Institutions: University of Kansas, The University of Melbourne
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162432050