“…where each β q,d is the multiplicity of an eigenvalue of h q with order d, and ϕ d is the cyclotomic polynomial of degree d. The computation of the eigenspaces of the monodromy operators, i.e. the cyclic modules [C[t, t −1 ]/ϕ d ] β q,d appearing in (1), is a difficult question which has been intensively studied the last decades and approached by different techniques such as nonresonant conditions for local systems (see for intance [6,7]), multinets ( [16,30]), minimality of the complement( [28,32,34,36]), graphs ( [1], [27]), and also mixed Hodge structure ( [3,4,5,11,12,13,15]). Many progress have been done for braid arrangements ( [29]), graphic arrangements ( [20]) and real line arrangements ( [33,35]).…”