Homological Aspects of Hyperplane Arrangements

This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as Koszul and Lie algebra methods, homological techniques, and the Bernstein-Gelfand-Gelfand correspondence, all illustrated with concrete calculations. We also explore connections of arrangements to other areas, such as De Concini-Procesi wonderful models, the Feichtner-Yuzvinsky algebra of an atomic lattice, fatpoints and blowups of projective space, and plane curve singularities.

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Hyperplane arrangements and Milnor fibrations

Suciu¹

2014

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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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.Comment: 52 pages, 7 figures; accepted for publication in the Annales de la Facult\'e des Sciences de Toulous

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Homological Aspects of Hyperplane Arrangements

Cited by 3 publications

References 38 publications

Geometry and Combinatorics of Resonant Weights

Geometry and Combinatorics of Resonant Weights

Hyperplane arrangements: computations and conjectures

Hyperplane arrangements and Milnor fibrations

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