{"paper":{"title":"Minimal Graded Free Resolutions for Monomial Curves Defined by Arithmetic Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Hema Srinivasan, Indranath Sengupta, Philippe Gimenez","submitted_at":"2011-08-16T11:01:06Z","abstract_excerpt":"Let $\\mm=(m_0,...,m_n)$ be an arithmetic sequence, i.e., a sequence of integers $m_0<...<m_n$ with no common factor that minimally generate the numerical semigroup $\\sum_{i=0}^{n}m_i\\N$ and such that $m_i-m_{i-1}=m_{i+1}-m_i$ for all $i\\in\\{1,...,n-1\\}$. The homogeneous coordinate ring $\\Gamma_\\mm$ of the affine monomial curve parametrically defined by $X_0=t^{m_0},...,X_n=t^{m_n}$ is a graded $R$-module where $R$ is the polynomial ring $k[X_0,...,X_n]$ with the grading obtained by setting $\\deg{X_i}:=m_i$. In this paper, we construct an explicit minimal graded free resolution for $\\Gamma_\\mm$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3203","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"}