Year: 2026
Type: preprint
Abstract: We prove that a nonconstant polynomial $f\in\mathbb{C}[x_1,x_2,x_3]$ is cylindrical (that is, $f\in\mathbb{C}[x_1,x_2]$ after an invertible linear change of coordinates) if and only if its bordered Hessian determinant vanishes identically. The same conclusion holds over $\mathbb{R}$. We also give explicit counterexamples to this criterion in every dimension $n\ge4$.
Source: arXiv (Cornell University)
Author: Lin, Xiaojin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212057513