On the Classification of Quasihomogeneous Functions

Details On the Classification of Quasihomogeneous Functions On the Classification of Quasihomogeneous Functions

1992-02-12

arxiv.org/abs/hep-th/9202039v1

Commun.Math.Phys. 150 (1992) 137

Physics

High Energy Physics

High Energy Physics - Theory

12 pages

Scientific paper

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 Poincar\'e 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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