{"paper":{"title":"Periodic Occurance of Complete Intersection Monomial Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"A. V. Jayanthan, Hema Srinivasan","submitted_at":"2012-03-09T04:49:37Z","abstract_excerpt":"We study the complete intersection property of monomial curves in the family $\\Gamma_{\\aa + \\jj} = {(t^{a_0 + j}, t^{a_1+j},..., t^{a_n + j}) ~ | ~ j \\geq 0, ~ a_0 < a_1 <...< a_n}$. We prove that if $\\Gamma_{\\aa+\\jj}$ is a complete intersection for $j \\gg0$, then $\\Gamma_{\\aa+\\jj+\\underline{a_n}}$ is a complete intersection for $j \\gg 0$. This proves a conjecture of Herzog and Srinivasan on eventual periodicity of Betti numbers of semigroup rings under translations for complete intersections. We also show that if $\\Gamma_{\\aa+\\jj}$ is a complete intersection for $j \\gg 0$, then $\\Gamma_{\\aa}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1991","kind":"arxiv","version":3},"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"}