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On Coxeter algebraic varieties

On Coxeter algebraic varieties We give a new method relying on Coxeter chambers for the geometrical description of real algebraic varieties invariant under the $$CB_{n}$$ CB n -Coxeter group. It turns out that the maximal number of connected components that a  $$CB_{n}$$ CB n -quartic algebraic variety can achieve is $$2^{n}+1$$ 2 n + 1 for specific coefficients. Our approach establishes a deep connection between the construction of $$CB_{n}$$ CB n -polynomials using partitions of integers and the geometrical aspect of the corresponding algebraic varieties. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Semesterberichte Springer Journals

On Coxeter algebraic varieties

Mathematische Semesterberichte , Volume 66 (1) – May 28, 2018

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References (51)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0720-728X
eISSN
1432-1815
DOI
10.1007/s00591-018-0221-z
Publisher site
See Article on Publisher Site

Abstract

We give a new method relying on Coxeter chambers for the geometrical description of real algebraic varieties invariant under the $$CB_{n}$$ CB n -Coxeter group. It turns out that the maximal number of connected components that a  $$CB_{n}$$ CB n -quartic algebraic variety can achieve is $$2^{n}+1$$ 2 n + 1 for specific coefficients. Our approach establishes a deep connection between the construction of $$CB_{n}$$ CB n -polynomials using partitions of integers and the geometrical aspect of the corresponding algebraic varieties.

Journal

Mathematische SemesterberichteSpringer Journals

Published: May 28, 2018

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