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December 2006 $\mathcal{D}$-Modules and Arrangements of Hyperplanes
Francisco James LEÓN TRUJILLO
Tokyo J. Math. 29(2): 429-444 (December 2006). DOI: 10.3836/tjm/1170348177

Abstract

Let $\mathcal{A}$ be a central arrangement of hyperplanes in $\mathbb{C}^n$ defined by the homogeneous polynomial $d_{\mathcal{A}}$. Let $D_n$ be the Weyl algebra of rank $n$ over $\mathbb{C}$ and let $P=\mathbb{C}[x_1,\ldots ,x_n,d_{\mathcal{A}}^{-1}]$ be the algebra of rational functions on the variety $Y_{\mathcal{A}}=\mathbb{C}^n\setminus \bigcup_{H\in \mathcal{A}}H$. Studying the structure of $P$ as a $D_n$-module we obtain a sequence of new $D_n$-modules. These modules allow us to define useful complexes that determine the De Rham cohomology of $Y_{\mathcal{A}}=\mathbb{C}^n\setminus \bigcup_{H\in \mathcal{A}}H$. Finally we compute the Poincaré series of $P$.

Citation

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Francisco James LEÓN TRUJILLO. "$\mathcal{D}$-Modules and Arrangements of Hyperplanes." Tokyo J. Math. 29 (2) 429 - 444, December 2006. https://doi.org/10.3836/tjm/1170348177

Information

Published: December 2006
First available in Project Euclid: 1 February 2007

zbMATH: 1140.32020
MathSciNet: MR2284982
Digital Object Identifier: 10.3836/tjm/1170348177

Subjects:
Primary: 32S22
Secondary: 13D40, 13N10, 52C35

Rights: Copyright © 2006 Publication Committee for the Tokyo Journal of Mathematics

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