1992/02/12 by Maximilian Kreuzer, Harald Skarke · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/bf02096569
published as Commun.Math.Phys. 150 (1992) 137 · 12 pages
arxiv created 1992/02/12 · arxiv updated 2015/06/26
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.