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
Mathematische Semesterberichte – Springer Journals
Published: May 28, 2018
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