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Journal of the London Mathematical Society 1995 51(1):105-119; doi:10.1112/jlms/51.1.105
© 1995 by London Mathematical Society
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© The London Mathematical Society

On Milnor Fibrations of Arrangements

Daniel C. Cohen and Alexander I. Suciu

Department of Mathematics, University of California Davis, California 95616-8633, USA E-mail: cohen{at}math.ucdavis.edu
Department of Mathematics, Northeastern University Boston, Massachusetts 02115, USA E-mail: alexsuciu{at}neu.edu

Received 15 April 1993.

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 C3, 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.

The second author was partially supported by N.S.F. grant DMS-9103556.


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