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arXiv · 1809.05026

A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups

Takuro Abe·Gerhard Röhrle·Christian Stump·Masahiko Yoshinaga
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Abstract

Given an irreducible well-generated complex reflection group, we construct an explicit basis for the module of vector fields with logarithmic poles along its reflection arrangement. This construction yields in particular a Hodge filtration of that module. Our approach is based on a detailed analysis of a flat connection applied to the primitive vector field. This generalizes and unifies analogous results for real reflection groups.

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Takuro Abe, Gerhard Röhrle, Christian Stump, Masahiko Yoshinaga. 2018-09-13. A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups. https://arxiv.org/abs/1809.05026

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