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On the classification of quasihomogeneous functions. (English) Zbl 0767.57019
We give a criterion for the existence of a non-degenerate quasi- homogeneous polynomial 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 possible sets of weights (up to the possibility of adding trivial variables) for a given value of the highest weight in the local algebra. For the value 3, which is of particular interest in string theory, a constructive version of this proof implies an algorithm for the calculation of all sets of weights allowing non-degeneracy.
Reviewer: M.Kreuzer

MSC:
57R45 Singularities of differentiable mappings in differential topology
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
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