{"paper":{"title":"Resolutions of 2 and 3 dimensional rings of invariants for cyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"David L. Wehlau, John C. Harris","submitted_at":"2011-10-23T17:35:47Z","abstract_excerpt":"Let $G$ be the cyclic group of order $n$ and suppose ${\\bf F}$ is a field containing a primitive $n^\\text{th}$ root of unity. We consider the ring of invariants ${\\bf F}[W]^G$ of a three dimensional representation $W$ of $G$ where $G \\subset \\text{SL}(W)$. We describe minimal generators and relations for this ring and prove that the lead terms of the relations are quadratic. These minimal generators for the relations form a Gr\\\"obner basis with a surprisingly simple combinatorial structure. We describe the graded Betti numbers for a minimal free resolution of $F[W]^G$. The case where $W$ is an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5067","kind":"arxiv","version":2},"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"}