Arrangements, multiderivations, and adjoint quotient map of type ADE

Abstract

The first part of this paper is a survey on algebro-geometric aspects of sheaves of logarithmic vector fields of hyperplane arrangements. In the second part we prove that the relative de Rham cohomology (of degree two) of ADE-type adjoint quotient map is naturally isomorphic to the module of certain multiderivations. The isomorphism is obtained by the Gauss-Manin derivative of the Kostant-Kirillov form.

References in corpus (2)

• A generalized logarithmic module and duality of Coxeter multiarrangements
• Exponents of 2-multiarrangements and freeness of 3-arrangements