A generalized logarithmic module and duality of Coxeter multiarrangements

Abstract

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.

17 pages

References in corpus (1)

• Signed-eliminable graphs and free multiplicities on the braid arrangement

Cited by in corpus (5)

• Exponents of 2-multiarrangements and freeness of 3-arrangements
• Equivariant multiplicities of Coxeter arrangements and invariant bases
• Primitive filtrations of the modules of invariant logarithmic forms of Coxeter arrangements
• Arrangements, multiderivations, and adjoint quotient map of type ADE
• Bases for the derivation modules of two-dimensional multi-Coxeter arrangements and universal derivations