First homology groups of the Milnor fiber boundary for generic hyperplane arrangements in ℂ³

2024/04/02 by Sakumi Sugawara, Sugawara, Sakumi
Mathematics · #32S22 #32S55 #52C35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2404.01555

openalex publication_date 2024/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Milnor fiber boundary for hyperplane arrangements in ℂ³. This is one of the examples of non-isolated surface singularities, which are studied by Némethi--Szilárd. In this paper, we compute the first homology group of the Milnor fiber boundary for a generic arrangement, which gives an affirmative answer to the conjecture of Suciu. Also, we give an example of an arrangement with n hyperplanes, whose torsion part in the Milnor fiber boundary homology contains a direct summand other than ℤ_n, for certain value of n.

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