English

A generalized logarithmic module and duality of Coxeter multiarrangements

Commutative Algebra 2008-07-17 v1 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.0807.2552,
  title  = {A generalized logarithmic module and duality of Coxeter multiarrangements},
  author = {Takuro Abe},
  journal= {arXiv preprint arXiv:0807.2552},
  year   = {2008}
}

Comments

17 pages

R2 v1 2026-06-21T11:01:11.775Z