Twisted Alexander modules of hyperplane arrangement complements

Elduque, Eva

doi:10.1007/s13398-021-01008-4

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…a torsion R-module for all 0 ≤ j ≤ r − 1 a free R-module for j = r 0 otherwise, and, as explained in [12, Section 10.1] (cf. [11])…”

Section: Hyperplane Arrangementsmentioning

confidence: 99%

Eigenspace Decomposition of Mixed Hodge Structures on Alexander Modules

Elduque¹,

Cueto²

2021

Preprint

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In previous work jointly with Geske, Maxim and Wang, we constructed a mixed Hodge structure (MHS) on the torsion part of Alexander modules, which generalizes the MHS on the cohomology of the Milnor fiber for weighted homogeneous polynomials. The cohomology of a Milnor fiber carries a monodromy action, whose semisimple part is an isomorphism of MHS. The natural question of whether this result still holds for Alexander modules was then posed. In this paper, we give a positive answer to that question, which implies that the direct sum decomposition of the torsion part of Alexander modules into generalized eigenspaces is in fact a decomposition of MHS. We also show that the MHS on the generalized eigenspace of eigenvalue 1 can be constructed without passing to a suitable finite cover (as is the case for the MHS on the torsion part of the Alexander modules), and compute it under some purity assumptions on the base space.

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“…a torsion R-module for all 0 ≤ j ≤ r − 1 a free R-module for j = r 0 otherwise, and, as explained in [12, Section 10.1] (cf. [11])…”

Section: Hyperplane Arrangementsmentioning

confidence: 99%

Eigenspace Decomposition of Mixed Hodge Structures on Alexander Modules

Elduque¹,

Cueto²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…A be the corresponding arrangement complement, and U f the infinite cyclic cover induced by f : U → C * . By [11,Theorem 4], we have that H j (U f ; Q) is a torsion R-module for all j < n, a free R-module for j = n, and 0 for j > n.…”

Section: Introductionmentioning

confidence: 99%