an:00740337
Zbl 0814.32007
Cohen, Daniel C.; Suciu, Alexander I.
On Milnor fibrations of arrangements
EN
J. Lond. Math. Soc., II. Ser. 51, No. 1, 105-119 (1995).
00025315
1995
j
32S55 32S40 55N25 57M05 20F36
Milnor fiber; homogeneous polynomial; hyperplane arrangements; Betti numbers; algebraic monodromy
We use covering space theory and homology with local coefficients to study the Milnor fiber of a homogeneous polynomial. These techniques are applied in the context of hyperplane arrangements, yielding an explicit algorithm for computing the Betti numbers of the Milnor fiber of an arbitrary real central arrangement in \(\mathbb{C}^ 3\), as well as the dimensions of the eigenspaces of the algebraic monodromy. We also obtain combinatorial formulas for these invariants of the Milnor fiber of a generic arrangement of arbitrary dimension using these methods.
Daniel C.Cohen (Davis)