Arrangements, multiderivations, and adjoint quotient map of type ADE

Details Arrangements, multiderivations, and adjoint quotient map of type ADE Arrangements, multiderivations, and adjoint quotient map of type ADE

2010-09-27

arxiv.org/abs/1009.5298v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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