{"paper":{"title":"A Finiteness Property of Torus Invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Samuel Tenka, Stella Gastineau","submitted_at":"2015-10-28T15:13:07Z","abstract_excerpt":"In this paper the invariant subring $R_n$ of an algebraic torus $T=(\\mathbb{C}^\\times)^r$ acting on the multi-homogenous polynomial ring\n  $$S^{\\boxtimes n}=\\bigoplus_{d=0}^\\infty (S^{(d)})^{\\otimes n},$$ where $S^{(d)}$ is the $d$th graded piece of the polynomial ring $S=\\mathbb{C}[x_1,\\dots,x_k]$, is studied from the viewpoint of matrices whose entries sum to zero. Using these weight matrices we prove that there exists a $d_1$ such that for all positive integers $n$, the relations of the invariant subring $R_n$ are generated in multi-homogenous degree $\\leq d_1$. Grant: 0943832"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08337","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"}