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arXiv · 2609.28490

Reducibility and Diagonal Equality Strata for Finite Jacobi Pencils

Matthew Faust
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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 $m$.

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Matthew Faust. 2026-08-20. Reducibility and Diagonal Equality Strata for Finite Jacobi Pencils. https://arxiv.org/abs/2609.28490

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