The Milnor fiber boundary of an arrangement determines its combinatorics
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908695154130944 |
|---|---|
| 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 |