The mixed Hodge structure on the fundamental group of a complement of hyperplanes

Kawahara, Yukihito

doi:10.1016/s0166-8641(01)00046-3

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Cohomology Algebra and Twisted Cohomology1

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Cited by 4 publications

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“…Theorem 3.5 (Kawahara [28], Choudary-Dimca-Papadima [5]). For central arrangements, the cohomology ring H * (M A ), together with its natural 1-marking, determines the lattice L(A).…”

Section: Cohomology Algebra and Twisted Cohomologymentioning

confidence: 99%

A survey of combinatorial aspects in the topology of complex hyperplane arrangements

Măcinic¹

2009

Combinatorial Aspects of Commutative Algebra

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“…Theorem 3.5 (Kawahara [28], Choudary-Dimca-Papadima [5]). For central arrangements, the cohomology ring H * (M A ), together with its natural 1-marking, determines the lattice L(A).…”

Section: Cohomology Algebra and Twisted Cohomologymentioning

confidence: 99%

A survey of combinatorial aspects in the topology of complex hyperplane arrangements

Măcinic¹

2009

Combinatorial Aspects of Commutative Algebra

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On Matroids and Orlik-Solomon Algebras

Kawahara

2004

Ann. Combin.

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In this paper we axiomatize combinatorics of arrangements of affine hyperplanes, which is a generalization of matroids, called quasi-matroids. We show that quasi-matroids are equivalent to pointed matroids. On the other hand, the Orlik-Solomon (OS) algebra of a quasimatroid can be constructed. We prove that the OS algebra of a quasi-matroid is isomorphic to the direct image of the OS algebra of a matroid by the linear derivation.

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Some analogs of Zariski’s Theorem on nodal line arrangements

Choudary

Dimca

Papadima

2005

Algebr. Geom. Topol.

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For line arrangements in P 2 with nice combinatorics (in particular, for those which are nodal away the line at infinity), we prove that the combinatorics contains the same information as the fundamental group together with the meridianal basis of the abelianization. We consider higher dimensional analogs of the above situation. For these analogs, we give purely combinatorial complete descriptions of the following topological invariants (over an arbitrary field): the twisted homology of the complement, with arbitrary rank one coefficients; the homology of the associated Milnor fiber and Alexander cover, including monodromy actions; the coinvariants of the first higher non-trivial homotopy group of the Alexander cover, with the induced monodromy action.

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The mixed Hodge structure on the fundamental group of a complement of hyperplanes

Cited by 4 publications

References 13 publications

A survey of combinatorial aspects in the topology of complex hyperplane arrangements

A survey of combinatorial aspects in the topology of complex hyperplane arrangements

On Matroids and Orlik-Solomon Algebras

Some analogs of Zariski’s Theorem on nodal line arrangements

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