First homology groups of the Milnor fiber boundary for generic hyperplane arrangements in $\mathbb{C}^{3}$

Abstract: We study the Milnor fiber boundary for hyperplane arrangements in $\mathbb{C}^3$. This is one of the examples of non-isolated surface singularities, which are studied by N\'emethi--Szil\'ard. In this paper, we compute the first homology group of the Milnor fiber boundary for a generic arrangement and prove it is combinatorially determined. In particular, this gives the affirmative answer to the conjecture of Suciu.