On Coxeter algebraic varieties

On Coxeter algebraic varieties Math Semesterber https://doi.org/10.1007/s00591-018-0221-z MAT HE MATIK IN FORSCHUNG UND ANWE NDUNG The geometry of CB quartics N. C. Combe Received: 3 July 2017 / Accepted: 19 March 2018 © Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018 Abstract We give a new method relying on Coxeter chambers for the geometrical description of real algebraic varieties invariant under the CB -Coxeter group. It turns out that the maximal number of connected components that a CB -quartic algebraic variety can achieve is 2 C 1 for specific coefficients. Our approach establishes a deep connection between the construction of CB -polynomials using partitions of integers and the geometrical aspect of the corresponding algebraic varieties. Keywords Real algebraic varieties · Coxeter group · Invariant theory · Chambers · Mirrors Mathematics Subject Classification Primary: 14R20 · 14J10 · Secondary: 14J70 · 14L24 · 15A03 · 15A18 1 Introduction 1.1 Motivation Let us briefly mention some historical results of relevance to this paper. The study was supported by a grant from the Labex Archimede and of the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the “Investissements d’Avenir” French Government programme managed by the French National Research Agency (ANR). First of all I wish to thank the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Semesterberichte Springer Journals

On Coxeter algebraic varieties

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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
D.O.I.
10.1007/s00591-018-0221-z
Publisher site
See Article on Publisher Site

Abstract

Math Semesterber https://doi.org/10.1007/s00591-018-0221-z MAT HE MATIK IN FORSCHUNG UND ANWE NDUNG The geometry of CB quartics N. C. Combe Received: 3 July 2017 / Accepted: 19 March 2018 © Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018 Abstract We give a new method relying on Coxeter chambers for the geometrical description of real algebraic varieties invariant under the CB -Coxeter group. It turns out that the maximal number of connected components that a CB -quartic algebraic variety can achieve is 2 C 1 for specific coefficients. Our approach establishes a deep connection between the construction of CB -polynomials using partitions of integers and the geometrical aspect of the corresponding algebraic varieties. Keywords Real algebraic varieties · Coxeter group · Invariant theory · Chambers · Mirrors Mathematics Subject Classification Primary: 14R20 · 14J10 · Secondary: 14J70 · 14L24 · 15A03 · 15A18 1 Introduction 1.1 Motivation Let us briefly mention some historical results of relevance to this paper. The study was supported by a grant from the Labex Archimede and of the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the “Investissements d’Avenir” French Government programme managed by the French National Research Agency (ANR). First of all I wish to thank the

Journal

Mathematische SemesterberichteSpringer Journals

Published: May 28, 2018

References

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