{"paper":{"title":"On the Hyperhomology of the Small Gobelin in Codimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Luis N\\'u\\~nez-Betancourt, Xavier G\\'omez-Mont","submitted_at":"2014-05-22T16:01:11Z","abstract_excerpt":"Given a zero-dimensional Gorenstein algebra $\\mathbb{B}$ and two syzygies between two elements $f_1,f_2\\in\\mathbb{B}$, one constructs a double complex of $\\mathbb{B}$-modules, ${\\cal G}_\\mathbb{B},$ called the small Gobelin. We describe an inductive procedure to construct the even and odd hyperhomologies of this complex. For high degrees, the difference $\\dim \\mathbb{H}_{j+2}({\\cal G}_\\mathbb{B}) - \\dim\\mathbb{H}_j({\\cal G}_\\mathbb{B})$ is constant, but possibly with a different value for even and odd degrees. We describe two flags of ideals in $\\mathbb{B}$ which codify the above differences o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5806","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"}