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Mathematics > Algebraic Geometry

arXiv:1807.00333 (math)
[Submitted on 1 Jul 2018 (v1), last revised 9 Jul 2018 (this version, v3)]

Title:Rank one local systems on complements of hyperplanes and Aomoto complexes

Authors:Morihiko Saito
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Abstract:We show that the cohomology of a rank 1 local system on the complement of a projective hyperplane arrangement can be calculated by the Aomoto complex in certain cases even if the condition on the sum of the residues of connection due to Esnault et al is not satisfied. For this we have to study the localization of Hodge-logarithmic differential forms which are defined by using an embedded resolution of singularities. As an application we can compute certain monodromy eigenspaces of the first Milnor cohomology group of the defining polynomial of the reflection hyperplane arrangement of type $G_{31}$ without using a computer.
Comments: 22 page
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1807.00333 [math.AG]
  (or arXiv:1807.00333v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.00333

Submission history

From: Morihiko Saito [view email]
[v1] Sun, 1 Jul 2018 14:04:33 UTC (19 KB)
[v2] Wed, 4 Jul 2018 17:17:42 UTC (20 KB)
[v3] Mon, 9 Jul 2018 13:08:07 UTC (21 KB)
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