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Homogeneous Milnor fibers and Kato--Matsumoto bounds via simplicial multiwedges
Abstract
For every n≥ 3 and s≥ 2, we construct a homogeneous polynomial of degree n(n+1)/2 whose Milnor fiber is exactly 2s-connected and whose rational cohomology contains a strictly defined nontrivial n-fold Massey product on classes of degree 2s+1, implying that the Milnor fiber is non-formal, while attaining the Kato--Matsumoto connectivity bound. Our construction is based on the simplicial multiwedges of the nerve complexes of simple polytopes introduced by Limonchenko, combined with Suciu's realization of weighted homogeneous Milnor fibers. We thereby answer two problems posed by Suciu.
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BibTeX
@misc{ishikawa2026homogeneous,
title = {{Homogeneous Milnor fibers and Kato--Matsumoto bounds via simplicial multiwedges}},
author = {Masaharu Ishikawa and Tat-Thang Nguyen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11396},
eprint = {2609.11396},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11396},
}
RIS
TY - UNPB
TI - Homogeneous Milnor fibers and Kato--Matsumoto bounds via simplicial multiwedges
AU - Masaharu Ishikawa
AU - Tat-Thang Nguyen
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11396
UR - https://arxiv.org/abs/2609.11396
AB - For every n≥ 3 and s≥ 2, we construct a homogeneous polynomial of degree n(n+1)/2 whose Milnor fiber is exactly 2s-connected and whose rational cohomology contains a strictly defined nontrivial n-fold Massey product on classes of degree 2s+1, implying that the Milnor fiber is non-formal, while attaining the Kato--Matsumoto connectivity bound. Our construction is based on the simplicial multiwedges of the nerve complexes of simple polytopes introduced by Limonchenko, combined with Suciu's realization of weighted homogeneous Milnor fibers. We thereby answer two problems posed by Suciu.
ER -