Hyperplane arrangements with non-formal Milnor fibers
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912951655464960 |
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| author | Suciu, Alexander I. |
| author_facet | Suciu, Alexander I. |
| contents | Each complex hyperplane arrangement $\mathcal{A}$ gives rise to a Milnor fibration of its complement. Building on work of Zuber, we give a combinatorial sufficient condition for the Milnor fiber $F(\mathcal{A})$ to be non-$1$-formal, expressed in terms of the multinet structure on $\mathcal{A}$, and use it to produce an infinite family of monomial arrangements $\mathcal{A}(3k,3k,3)$ with non-formal Milnor fibers. We also review the relevant background on cohomology jump loci, formality, and the topology of Milnor fibers of arrangements. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_07301 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hyperplane arrangements with non-formal Milnor fibers Suciu, Alexander I. Algebraic Topology Algebraic Geometry Combinatorics 32S55, 14C21, 14F35, 20F55, 32S22, 32S35, 55N25, 57M10 Each complex hyperplane arrangement $\mathcal{A}$ gives rise to a Milnor fibration of its complement. Building on work of Zuber, we give a combinatorial sufficient condition for the Milnor fiber $F(\mathcal{A})$ to be non-$1$-formal, expressed in terms of the multinet structure on $\mathcal{A}$, and use it to produce an infinite family of monomial arrangements $\mathcal{A}(3k,3k,3)$ with non-formal Milnor fibers. We also review the relevant background on cohomology jump loci, formality, and the topology of Milnor fibers of arrangements. |
| title | Hyperplane arrangements with non-formal Milnor fibers |
| topic | Algebraic Topology Algebraic Geometry Combinatorics 32S55, 14C21, 14F35, 20F55, 32S22, 32S35, 55N25, 57M10 |
| url | https://arxiv.org/abs/2603.07301 |