The Milnor fiber boundary of an arrangement determines its combinatorics
Algebraic Geometry
2025-12-08 v1 Combinatorics
Geometric Topology
Abstract
The boundary of the Milnor fiber associated with a complex line arrangement is a three dimensional plumbed manifold, and it is a combinatorial invariant. We prove the reverse implication, which was conjectured N\'emethi and Szil\'ard. That is, this boundary of the Milnor fiber determines the combinatorics of the arrangement. Furthermore, we give an explicit method which constructs the poset associated with the arrangement, given a plumbing graph in normal form for the boundary.
Cite
@article{arxiv.2512.05891,
title = {The Milnor fiber boundary of an arrangement determines its combinatorics},
author = {Baldur Sigurðsson and Juan Viu-Sos},
journal= {arXiv preprint arXiv:2512.05891},
year = {2025}
}
Comments
20 pages, 10 figures