Spectral pairs of Newton non-degenerate polynomials with isolated singularities

Abstract

We give a formula for the spectral pairs of Newton non-degenerate polynomials with isolated singularities. This is a revised version of a conjecture proposed by Steenbrink fifty years ago. Although this conjecture fails in the non-simplicial Newton polytope case, we can find the correction term using the intersection complexes and the primitive intersection cohomologies of toric varieties associated with non-simplicial compact faces. To verify the correctness of the formula, we provide a sample code for Singular which computes the spectral pairs and compares the output with that of sppairs in Singular for the three variable case.