Torsion formula for H1(∂F,Z) of the Milnor fiber boundary of hyperplane arrangements

Determine a general formula for the torsion subgroup of the first integral homology group H1(∂F, Z), where ∂F denotes the Milnor fiber boundary associated to a complex hyperplane arrangement A in C^3 (equivalently, a line arrangement in CP^2).

Background

This paper studies the Milnor fiber boundary ∂F of hyperplane arrangements as examples of non-isolated surface singularities. For such arrangements, the first Betti number b1(∂F) is known to be combinatorially determined, but a general combinatorial description of the integral first homology H1(∂F, Z), in particular its torsion subgroup, has remained unresolved.

Motivated by Problem 24.4.19 in Némethi–Szilárd, the author formulates Problem 1.2, asking for a formula for the torsion in H1(∂F, Z). The paper resolves this question in the special case of generic arrangements by computing H1(∂F, Z) explicitly and confirming a conjecture of Suciu, but the general problem for arbitrary arrangements remains open.