On the classification of quasihomogeneous functions
Copyright policy )On the classification of quasihomogeneous functions
We give a criterion for the existence of a non-degenerate 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.
12 pages
- TU Wien Austria
- European Organization for Nuclear Research Switzerland
High Energy Physics - Theory, 14B05, 32S05, existence of a non-degenerate quasi- homogeneous polynomial with a fixed set of weights, FOS: Physical sciences, Theory of singularities and catastrophe theory, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Poincaré polynomial, highest weight in the local algebra, Differentiable maps on manifolds, High Energy Physics - Theory (hep-th), 81T40, weighted projective space, 32S10, Singularities of differentiable mappings in differential topology
High Energy Physics - Theory, 14B05, 32S05, existence of a non-degenerate quasi- homogeneous polynomial with a fixed set of weights, FOS: Physical sciences, Theory of singularities and catastrophe theory, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Poincaré polynomial, highest weight in the local algebra, Differentiable maps on manifolds, High Energy Physics - Theory (hep-th), 81T40, weighted projective space, 32S10, Singularities of differentiable mappings in differential topology
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