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On Thom Polynomials for 𝒜-singularities of parametric curves and degeneracy loci formulas
Abstract
In this research article, we make an in-depth investigation of the computations for Thom Polynomials for 𝒜-singularities of parametric curves germs in the plane and space cases using the framework established by Ohmoto and the Restriction Method introduced by Rimányi, and we also propose a geometric way for such computations using degeneracy loci Chern classes formulas proven by Fulton, which seems a promising way to generalize the Thom Polynomial expression for the stabilization of such singularities in ℂN, depending exclusively on N as a parameter.
Related
- Probability-theoretic interpretation of degeneracy locus formulas
- Parametric Families of Minimal Positive Cubature Formulas of Degrees 4 and 6 on the 2-Sphere
- Strict Separation of Antiperiodic Degeneracy Curves for Elliptic Euler and Lagrangian Solutions
- Euler-Maclaurin formulas for polynomials on the Cubed Sphere
- New Formulas of Bernoulli Polynomials of the Second Kind Using Several Approaches
BibTeX
@misc{pissolato2026thom,
title = {{On Thom Polynomials for $\mathcalA$-singularities of parametric curves and degeneracy loci formulas}},
author = {João Vítor Pissolato},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35922},
eprint = {2610.35922},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35922},
}
RIS
TY - UNPB
TI - On Thom Polynomials for 𝒜-singularities of parametric curves and degeneracy loci formulas
AU - João Vítor Pissolato
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.35922
UR - https://arxiv.org/abs/2610.35922
AB - In this research article, we make an in-depth investigation of the computations for Thom Polynomials for 𝒜-singularities of parametric curves germs in the plane and space cases using the framework established by Ohmoto and the Restriction Method introduced by Rimányi, and we also propose a geometric way for such computations using degeneracy loci Chern classes formulas proven by Fulton, which seems a promising way to generalize the Thom Polynomial expression for the stabilization of such singularities in ℂ^N, depending exclusively on N as a parameter.
ER -