Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Combe, N.
Mathematische Semesterberichte , Volume 66 (1) – May 28, 2018
Download PDF
15 pages

Loading next page...
 
/lp/springer_journal/on-coxeter-algebraic-varieties-g3mbd0JKD7
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 Semesterberichte – Springer Journals

Published: May 28, 2018

References

  • Two projective surfaces with many nodes, admitting the symmetries of the icosahedron
    Barth, W
  • Complex algebraic surfaces
    Beauville, A
  • The classification of quadrics
    Bromwich, TJI
  • A classification of quadrics in affine n‑space by mean of arithmetic invariant
    Buringthon, RS
  • Sulla “piccola variazione” di uma curva piana algebrica reale
    Brusotti, L
  • Colloquium De Giorgi 2013 and 2014. Lectures from the colloquium, Scuola Normale Superiore, Pisa, Italy, 2013 and 2014
    Catanese, F
  • Topological methods in moduli theory
    Catanese, F
  • Complex surfaces of general type: some recent progress ArXiv:math/0602477v1
    Bauer, I; Catanese, F; Pignatelli, R
  • Babbage’s conjecture, contact of surfaces, symmetric determinantal varieties and applications
    Catanese, F
  • Mémoire sur les courbes du troisième ordre
    Cayley, A
  • Topologie de certains espaces de plongements
    Cerf, J
  • Ueber die Anwendung der Abelschen Functionen in der Geometrie
    Clebsch, A
  • Étude de la connexité des surfaces algébriques réelles, Éditions Universitaires Européennes
    Combe, NC
  • Geometric classification of real ternary octahedral quartics
    Combe, NC
  • Cohomology of Artin groups: Addendum: “The homotopy type of Artin groups”
    Concini, C; Salvetti, M
  • Fondamenti per la geometria sopra le superificie rationali del punto di vista reale
    Comesatti, A
  • Arithmetic on singular cubic surfaces
    Coray, DF
  • Algebraic points on cubic hypersurfaces
    Coray, DF
  • Cours de géometrie algébrique
    Coray, D
  • Les immeubles des groupes de tresses généralisés
    Deligne, P
  • Séminaires Henri Cartan, 14, exposés
    Douady, A
  • Algebraic surfaces with pg = g = 0, Algebraic Surfaces, CIME 1977
    Dolgachev, I
  • A projective surface of degree eight with 168 nodes
    Endrass, S
  • Etude des surfaces qui admettent tous les plans de symétrie d’un polyèdre régulier
    Goursat, E
  • Algebraic geometry and geometric modeling
    Holzer, S; Labs, O
  • Reflection groups and Coxeter groups
    Humphreys, JE
  • Uber die Flachen vierten Grades mit sechzehn singularen Punkten
    Kummer, EE
  • A septic with 99 real nodes
    Labs, O
  • Fake real planes: exotic affine algebraic models of R2
    Mangolte, F; Dubouloz, A
  • Cremona groups of real surfaces in “Automorphisms in Birational and Affine Geometry”
    Mangolte, F; Blanc, J
  • Geometrically rational real conic bundles and very transitive actions
    Mangolte, F; Blanc, J
  • Classical invariant theory
    Olver, P
  • Polynomial invariants of finite groups a survey of recent developments
    Smith, L
  • A geometrical construction for the polynomial invariants of some reflection groups
    Sarti, A
  • Symmetrische Flachen mit Gewohnlichen Doppelpunkte
    Sarti, A
  • Topology of the complement of real hyperplanes in CN
    Salvetti, M
  • The homotopy type of Artin groups
    Salvetti, M
  • On the distribution of surfaces of the third order into species
    Schläfli, L
  • The non-singular cubic surfaces
    Segre, B
  • Una notevole superficie di 5o ordine con soli punti doppi isolati
    Togliatti, E