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On Milnor Fibrations of Arrangements
Author(s) -
Cohen Daniel C.,
Suciu Alexander I.
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/51.1.105
Subject(s) - monodromy , mathematics , hyperplane , betti number , context (archaeology) , pure mathematics , dimension (graph theory) , homogeneous , algebraic number , fiber , polynomial , homology (biology) , algebra over a field , combinatorics , mathematical analysis , organic chemistry , paleontology , biochemistry , chemistry , gene , biology
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 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.