A generalized logarithmic module and duality of Coxeter multiarrangements
Preprint Series # 919
Abe, Takuro A generalized logarithmic module and duality of Coxeter multiarrangements. (2008);
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
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
|Uncontrolled Keywords:||arrangement of hyperplanes, multiarrangement, logarithmic derivation module, logarithmic differential module, Coxeter group|
|Subjects:||32-xx SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES|