On Milnor Fibrations of Arrangements

Cohen, Daniel C.; Suciu, Alexander I.

doi:10.1112/jlms/51.1.105

Cited by 75 publications

(120 citation statements)

References 10 publications

Supporting

Mentioning

118

Contrasting

Order By: Relevance

“…Let = Tm = Tk, see [5]. In this section, we prove the following strengthening of a result of Massey [21].…”

mentioning

confidence: 66%

See 1 more Smart Citation

Nonresonance conditions for arrangements

Cohen¹,

Dimca²,

Orlik³

2003

Annales De L’institut Fourier

Self Cite

View full text Add to dashboard Cite

show abstract

“…Let = Tm = Tk, see [5]. In this section, we prove the following strengthening of a result of Massey [21].…”

mentioning

confidence: 66%

“…Consequently, this notion makes sense for both affine and projective arrangements. Let [23], [24], [25] In the case when ,C is a rank one complex local system arising in the context of the Milnor fiber associated to ,A (see [5] and Section 5 below), this result was obtained by Libgober [20]. We '[7~] is a perverse sheaf on M(A).…”

mentioning

confidence: 99%

Nonresonance conditions for arrangements

Cohen¹,

Dimca²,

Orlik³

2003

Annales De L’institut Fourier

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this section, we review some facts concerning the Milnor fibration of a complex (multi)-arrangement of hyperplanes, following [5] and [9].…”

Section: Homology Of the Milnor Fiber Of A Multi-arrangementmentioning

confidence: 99%

“…See [12], [19], [14] in the context of 2-complexes; [5] in the context of cyclic covers of complements of arrangements; and [2] in an algebraic setting. For completeness, we will sketch a proof of the version needed here.…”

Section: Theorem 2 Letmentioning

confidence: 99%

Torsion in Milnor fiber homology

Cohen

Denham

Suciu

2003

Algebr. Geom. Topol.

View full text Add to dashboard Cite

In a recent paper, Dimca and Némethi pose the problem of finding a homogeneous polynomial f such that the homology of the complement of the hypersurface defined by f is torsion-free, but the homology of the Milnor fiber of f has torsion. We prove that this is indeed possible, and show by construction that, for each prime p, there is a polynomial with p-torsion in the homology of the Milnor fiber. The techniques make use of properties of characteristic varieties of hyperplane arrangements.

show abstract

“…For instance, local systems may be used to study the Milnor fiber of the non-isolated hypersurface singularity at the origin obtained by coning the arrangement; see [8,5]. In mathematical physics, local systems on complements of arrangements arise in the Aomoto-Gelfand theory of multivariable hypergeometric integrals [2,12,18] and the representation theory of Lie algebras and quantum groups.…”

Section: Introductionmentioning

confidence: 99%