Modular equalities for complex reflection arrangements

A computational approach to Milnor fiber cohomology

“…The monomial arrangement A(m, m, 3). The case of complex reflexion arrangements is discussed in [28], where the authors prove in particular the following result.…”

“…For an eigenvalue of order p s , the papers [33], [28] give also upper bounds for the corresponding multiplicities for any line arrangement, see also [4], [5]. However, for the monomial arrangements, the existence of eigenvalues of order 6 (resp.…”

On the Milnor Monodromy of the Irreducible Complex Reflection Arrangements

“…When G is an irreducible complex reflection group, already to determine the first possibly non-trivial monodromy operator h 1 (G) : H 1 (F (G), C) → H 1 (F (G), C) is a challenge. In a recent preprint [22], A. Mȃcinic, S. Papadima and R. Popescu have obtained a nearly complete control on the eigenvalues of the monodromy operator h 1 (G) of order p s , with p a prime number and s a positive integer. Some of their main results are stated below, see Theorems 1.1, 1.2 and 1.3, in order to better understand the contribution of our note.…”

“…For s = 1, this inequality becomes an equality. Denote by F (m, 1, n) the Milnor fiber of the full monomial arrangement A(m, 1, n), and recall the following result proved in [22].…”

On Algebraic Surfaces Associated with Line Arrangements

“…We also compute the Chern ratio. This numerical invariant is of special interest for algebraic surfaces, see for instance [16], [17], [18], [22].…”