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The Poincaré polynomial of an mp arrangement


Author: Chris Macmeikan
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1575-1580
MSC (2000): Primary 14F25; Secondary 14R20
DOI: https://doi.org/10.1090/S0002-9939-04-07398-8
Published electronically: January 20, 2004
MathSciNet review: 2051116
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Abstract: Let $\mathcal{A}=\{A_i\}_{i\in I}$ be an mp arrangement in a complex algebraic variety $X$ with corresponding complement $Q(\mathcal{A})=X\backslash\bigcup_{i\in I}A_{i}$ and intersection poset $L(\mathcal{A})$. Examples of such arrangements are hyperplane arrangements and toral arrangements, i.e., collections of codimension 1 subtori, in an algebraic torus. Suppose a finite group $\Gamma$ acts on $X$ as a group of automorphisms and stabilizes the arrangement $\{A_i\}_{i\in I}$ setwise. We give a formula for the graded character of $\Gamma$ on the cohomology of $Q(\mathcal{A})$ in terms of the graded character of $\Gamma$ on the cohomology of certain subvarieties in $L(\mathcal{A})$.


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Additional Information

Chris Macmeikan
Affiliation: Tokyo University of Science, Noda, Chiba 278-8510, Japan
Address at time of publication: Department of Mathematics, Keio University, Hiyoshi, Kohoku, Yokohama 223-8522, Japan
Email: chris_macmeikan@ma.noda.tus.ac.jp, chris@math.keio.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-04-07398-8
Received by editor(s): May 28, 2002
Received by editor(s) in revised form: January 7, 2003
Published electronically: January 20, 2004
Additional Notes: This research was partially supported by an Australian Research Council grant for the project “Group Representation Theory and Cohomology of Algebraic Varieties”
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society

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