{"paper":{"title":"Polynomial degree bounds for matrix semi-invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.RT","authors_text":"Harm Derksen, Visu Makam","submitted_at":"2015-12-10T20:12:47Z","abstract_excerpt":"We study the left-right action of $\\operatorname{SL}_n \\times \\operatorname{SL}_n$ on $m$-tuples of $n \\times n$ matrices with entries in an infinite field $K$. We show that invariants of degree $n^2- n$ define the null cone. Consequently, invariants of degree $\\leq n^6$ generate the ring of invariants if $\\operatorname{char}(K)=0$. We also prove that for $m \\gg 0$, invariants of degree at least $n\\lfloor \\sqrt{n+1}\\rfloor$ are required to define the null cone. We generalize our results to matrix invariants of $m$-tuples of $p\\times q$ matrices, and to rings of semi-invariants for quivers. For"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03393","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"}