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Whitney fold and cusp for algebraic surfaces, and singularities of discriminants

  • Alexander Esterov
  • Lev Vladimirov
  • Aliaksandr Yuran
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Abstract

We describe transversal singularity types of the singular locus of the A-discriminant for A⊂ℤ, and deduce a Whitney type theorem for a coordinate projection of a surface defined by a general polynomial equation with a given Newton polytope N: under mild combinaorial conditions on N, all multisingularities are stable (folds, cusps, and double folds). We then enumerate the multisingularities in terms of N. The results rely on the analysis of degeneracy of relevant Vandermonde/Schur type matrices, which may be of independent interest.

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Cite

BibTeXRIS
BibTeX
@misc{esterov2026whitney,
  title = {{Whitney fold and cusp for algebraic surfaces, and singularities of discriminants}},
  author = {Alexander Esterov and Lev Vladimirov and Aliaksandr Yuran},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.17448},
  eprint = {2609.17448},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.17448},
}
RIS
TY  - UNPB
TI  - Whitney fold and cusp for algebraic surfaces, and singularities of discriminants
AU  - Alexander Esterov
AU  - Lev Vladimirov
AU  - Aliaksandr Yuran
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.17448
UR  - https://arxiv.org/abs/2609.17448
AB  - We describe transversal singularity types of the singular locus of the A-discriminant for A⊂ℤ, and deduce a Whitney type theorem for a coordinate projection of a surface defined by a general polynomial equation with a given Newton polytope N: under mild combinaorial conditions on N, all multisingularities are stable (folds, cusps, and double folds). We then enumerate the multisingularities in terms of N. The results rely on the analysis of degeneracy of relevant Vandermonde/Schur type matrices, which may be of independent interest.
ER  -