Dept. Math, Hokkaido Univ. EPrints Server

A generalized logarithmic module and duality of Coxeter multiarrangements

Preprint Series # 919
Abe, Takuro A generalized logarithmic module and duality of Coxeter multiarrangements. (2008);

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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.

Item Type:Preprint
Additional Information:30
Uncontrolled Keywords:arrangement of hyperplanes, multiarrangement, logarithmic derivation module, logarithmic differential module, Coxeter group
Subjects:32-xx SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES
ID Code:1883