{"paper":{"title":"On the Jordan structure of holomorphic matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"J\\\"urgen Leiterer","submitted_at":"2017-03-28T12:25:34Z","abstract_excerpt":"Let $X$ be an open subset of $\\Bbb C^N$, and let $A$ be an $n\\times n$ matrix of holomorphic functions on $X$. We call a point $\\xi\\in X$ $\\mathbf{Jordan}$ $\\mathbf{stable}$ for $A$ if $\\xi$ is not a splitting point of the eigenvalues of $A$ and, moreover, there is a neighborhood $U$ of $\\xi$ such that, for each $1\\le k\\le n$, the number of Jordan blocks of size $k$ in the Jordan normal forms of $A(\\zeta)$ is the same for all $\\zeta\\in U$. H. Baumg\\\"artel (Analytic perturbation theory for matrices and operators, Birkh\\\"auser, 1985) proved that there is a nowhere dense closed analytic subset of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09535","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}