The Milnor fiber boundary of an arrangement determines its combinatorics

Fuente: arXiv
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Main Authors: Sigurðsson, Baldur, Viu-Sos, Juan
Format: Preprint
Published: 2025
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author Sigurðsson, Baldur
Viu-Sos, Juan
author_facet Sigurðsson, Baldur
Viu-Sos, Juan
contents 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 Némethi and Szilárd. 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_05891
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Milnor fiber boundary of an arrangement determines its combinatorics
Sigurðsson, Baldur
Viu-Sos, Juan
Algebraic Geometry
Combinatorics
Geometric Topology
32S22
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 Némethi and Szilárd. 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.
title The Milnor fiber boundary of an arrangement determines its combinatorics
topic Algebraic Geometry
Combinatorics
Geometric Topology
32S22
url https://arxiv.org/abs/2512.05891