Modular Equalities for Complex Reflection Arrangements
Anca Daniela MačinicSimion Stoilow Institute of Mathematics, P.O. Box 1-764, RO-014700 Bucharest, Romania
Ştefan PapadimaSimion Stoilow Institute of Mathematics, P.O. Box 1-764, RO-014700 Bucharest, Romania
Clement Radu PopescuSimion Stoilow Institute of Mathematics, unit no. 4, P.O. Box 1-764, RO-014700 Bucharest, Romania
We compute the combinatorial Aomoto-Betti numbers of a complex reflection arrangement. When has rank at least 3, we find that , for all primes . Moreover, if , and if and only if is the Hesse arrangement. We deduce that the multiplicity of an order eigenvalue of the monodromy action on the first rational homology of the Milnor fiber is equal to the corresponding Aomoto-Betti number, when is prime. We give a uniform combinatorial characterization of the property , for . We completely describe the monodromy action for full monomial arrangements of rank 3 and 4. We relate and to multinets, on an arbitrary arrangement.
Cite this article
Anca Daniela Mačinic, Ştefan Papadima, Clement Radu Popescu, Modular Equalities for Complex Reflection Arrangements. Doc. Math. 22 (2017), pp. 135–150DOI 10.4171/DM/561