ar X iv : 1 30 1 . 48 51 v 1 [ m at h . A G ] 2 1 Ja n 20 13 HYPERPLANE ARRANGEMENTS AND MILNOR FIBRATIONS
نویسنده
چکیده
— There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank 1 local systems on the complement of the arrangement to gain information on the homology of the other three spaces, and on the monodromy operators of the various fibrations.
منابع مشابه
Hyperplane Arrangements and Milnor Fibrations
— There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank 1 local systems on the complement of the arrangement to gain information on the h...
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Let G be a finite, complex reflection group acting on a complex vector space V , and δ its disciminant polynomial. The fibres of δ admit commuting actions of G and a cyclic group. The virtual G×Cm character given by the Euler characteristic of a fibre is a refinement of the zeta function of the geometric monodromy, calculated in [8]. We show that this virtual character is unchanged by replacing...
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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. ...
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تاریخ انتشار 2013