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On isotropic points and contact invariants of curves
Abstract
Let (Cf,0) ⊂ (ℂn,0) be a germ of an irreducible holomorphic curve, given implicity by f(x)=0 if n=2 and by f(x)=g(x)=0 if n=3, and parametrised by γ:(ℂ,0) → (ℂn,0). We define the contact invariants Isof and Isoγ for f and γ, respectively, which count the number of isotropic points that appear after a generic deformation of the curve. We first consider the case where the curve is regular and establish a relation between those invariants and the number of vertices, inflection points and the zero-torsion points (for n=3) that emerge from the deformation of the curve. Furthermore, we consider a germ of a singular curve with an isolated singularity and relate the number of isotropic points with the Milnor number of f
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BibTeX
@misc{falqueto2026isotropic,
title = {{On isotropic points and contact invariants of curves}},
author = {Amanda Dias Falqueto and Juan J. Nuño Ballesteros and Raúl Oset Sinha},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06440},
eprint = {2611.06440},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06440},
}
RIS
TY - UNPB
TI - On isotropic points and contact invariants of curves
AU - Amanda Dias Falqueto
AU - Juan J. Nuño Ballesteros
AU - Raúl Oset Sinha
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06440
UR - https://arxiv.org/abs/2611.06440
AB - Let (C_f,0) ⊂ (ℂ^n,0) be a germ of an irreducible holomorphic curve, given implicity by f(x)=0 if n=2 and by f(x)=g(x)=0 if n=3, and parametrised by γ:(ℂ,0) → (ℂ^n,0). We define the contact invariants Iso_f and Iso_γ for f and γ, respectively, which count the number of isotropic points that appear after a generic deformation of the curve. We first consider the case where the curve is regular and establish a relation between those invariants and the number of vertices, inflection points and the zero-torsion points (for n=3) that emerge from the deformation of the curve. Furthermore, we consider a germ of a singular curve with an isolated singularity and relate the number of isotropic points with the Milnor number of f
ER -