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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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Cite

BibTeXRIS
BibTeX
@misc{jung2026spectral,
  title = {{Spectral pairs of Newton non-degenerate polynomials with isolated singularities}},
  author = {Seung-Jo Jung and In-Kyun Kim and Morihiko Saito and Youngho Yoon},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03464},
  eprint = {2611.03464},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03464},
}
RIS
TY  - UNPB
TI  - Spectral pairs of Newton non-degenerate polynomials with isolated singularities
AU  - Seung-Jo Jung
AU  - In-Kyun Kim
AU  - Morihiko Saito
AU  - Youngho Yoon
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03464
UR  - https://arxiv.org/abs/2611.03464
AB  - 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.
ER  -