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On the classification of quasihomogeneous functions

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Abstract

We give a criterion for the existence of a non-degenerated quasihomogeneous polynomial in a configuration, i.e. in the space of polynomials with a fixed set of weights, and clarify the relation of this criterion to the necessary condition derived from the formula for the Poincaré polynomial. We further prove finiteness of the number of configurations for a given value of the singularity index. For the value 3 of this index, which is of particular interest in string theory, a constructive version of this proof implies an algorithm for the calculation of all non-degenerate configurations.

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Authors and Affiliations

  1. Theory Division, CERN, Ch-1211, Genera 23, Switzerland

    Maximillian Kreuzer

  2. Institut für Theoretische Physik, Technische Universitä Wien, Wiedner Hauptstrasse 8-10, A-1040, Wien, Austria

    Harald Skarke

Authors
  1. Maximillian Kreuzer
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  2. Harald Skarke
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Communicted by A. Connes

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Kreuzer, M., Skarke, H. On the classification of quasihomogeneous functions. Commun.Math. Phys. 150, 137–147 (1992). https://doi.org/10.1007/BF02096569

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  • DOI: https://doi.org/10.1007/BF02096569

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