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arXiv · 2611.03464

Spectral pairs of Newton non-degenerate polynomials with isolated singularities

Seung-Jo Jung·In-Kyun Kim·Morihiko Saito·Youngho Yoon
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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.

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Seung-Jo Jung, In-Kyun Kim, Morihiko Saito, Youngho Yoon. 2026-11-02. Spectral pairs of Newton non-degenerate polynomials with isolated singularities. https://arxiv.org/abs/2611.03464

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