First homology groups of the Milnor fiber boundary for generic hyperplane arrangements in C3C³

We study the Milnor fiber boundary for hyperplane arrangements in . 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 hyperplanes, whose torsion part in the Milnor fiber boundary homology contains a direct summand other than , for certain value of .