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Reducibility and Diagonal Equality Strata for Finite Jacobi Pencils
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≥4, 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.
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BibTeX
@misc{faust2026reducibility,
title = {{Reducibility and Diagonal Equality Strata for Finite Jacobi Pencils}},
author = {Matthew Faust},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28490},
eprint = {2609.28490},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28490},
}
RIS
TY - UNPB
TI - Reducibility and Diagonal Equality Strata for Finite Jacobi Pencils
AU - Matthew Faust
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.28490
UR - https://arxiv.org/abs/2609.28490
AB - 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≥4, 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.
ER -