Homology graph of real arrangements and monodromy of Milnor Fiber

We study the first homology group H-1(F,C) of the Milnor fiber F of sharp arrangements (A) over bar in P-R(2). Our work relies on the minimal complex C-*(S(A)) of the deconing arrangement A and its boundary map. We describe an algorithm which computes possible eigenvalues of the monodromy operator h(1) of H-1(F, C). We prove that, if a condition on some intersection points of lines in A is satisfied, then the only possible nontrivial eigenvalues of h(1) are cubic roots of the unity. Moreover we give sufficient conditions for just eigenvalues of order 3 or 4 to appear in cases in which this condition is not satisfied. (C) 2017 Elsevier Inc. All rights reserved.