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.
| Comments: | This is a preliminary version, 93 pages. Comments are very welcome |
| Subjects: | Algebraic Geometry (math.AG); Complex Variables (math.CV); Representation Theory (math.RT) |
| MSC classes: | 14C30, 32S35, 32C38 |
| Cite as: | arXiv:2605.25314 [math.AG] |
| (or arXiv:2605.25314v1 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25314 arXiv-issued DOI via DataCite (pending registration) |
From: Ruijie Yang [view email]
[v1]
Mon, 25 May 2026 00:31:03 UTC (109 KB)
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