Year: 2026
Type: preprint
Abstract: We study reducibility of the characteristic polynomials of a class of finite Jacobi pencils. We classify the diagonal equality patterns for which generic connected couplings yield reducibility and use this classification to prove that for $n\ge4$, the connected reducible locus has codimension at least two in the connected parameter space. For $n=2m+1$, we also prove that for every fixed connected coupling vector, the locus of diagonal potentials that admit a constant branch has codimension $m$.
Source: arXiv (Cornell University)
Author: Faust, Matthew
Institution: Michigan State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214276213