A generalized logarithmic module and duality of Coxeter multiarrangements

Details A generalized logarithmic module and duality of Coxeter multiarrangements A generalized logarithmic module and duality of Coxeter multiarrangements

2008-07-16

arxiv.org/abs/0807.2552v1

Mathematics

Commutative Algebra

17 pages

Scientific paper

We introduce a new definition of a generalized logarithmic module of multiarrangements by uniting those of the logarithmic derivation and the differential modules. This module is realized as a logarithmic derivation module of an arrangement of hyperplanes with a multiplicity consisting of both positive and negative integers. We consider several properties of this module including Saito's criterion and reflexivity. As applications, we prove a shift isomorphism and duality of some Coxeter multiarrangements by using the primitive derivation.

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