{"paper":{"title":"Exponential growth of rank jumps for A-hypergeometric systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Mar\\'ia-Cruz Fern\\'andez-Fern\\'andez","submitted_at":"2012-01-24T18:56:38Z","abstract_excerpt":"The dimension of the space of holomorphic solutions at nonsingular points (also called the holonomic rank) of a $A$--hypergeometric system $M_A (\\beta)$ is known to be bounded above by $ 2^{2d}\\operatorname{vol}(A)$, where $d$ is the rank of the matrix $A$ and $\\vol (A)$ is its normalized volume. This bound was thought to be very vast because it is exponential on $d$. Indeed, all the examples we have found in the literature verify that $\\operatorname{rank}(M_A (\\beta))<2 \\vol (A)$. We construct here, in a very elementary way, some families of matrices $A_{(d)}\\in \\ZZ^{d \\times n}$ and paramete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5090","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"}