{"paper":{"title":"Algebraic invariants of projective monomial curves associated to generalized arithmetic sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Eva Garc\\'ia-Llorente, Ignacio Garc\\'ia-Marco, Isabel Bermejo","submitted_at":"2015-12-02T09:06:41Z","abstract_excerpt":"Let $K$ be an infinite field and let $m_1,\\ldots,m_n$ be a generalized arithmetic sequence of positive integers, i.e., there exist $h, d, m_1 \\in\\mathbb{Z}^+$ such that $m_i = h m_1 + (i-1)d$ for all $i \\in \\{2,\\ldots,n\\}$. We consider the projective monomial curve $\\mathcal C\\subset \\mathbb{P}^{n}_{K}$ parametrically defined by $$x_1=s^{m_1}t^{m_n-m_1},\\dots,x_{n-1}=s^{m_{n-1}}t^{m_n-m_{n-1}},x_n=s^{m_n},x_{n+1}=t^{m_n}.$$ In this work, we characterize the Cohen-Macaulay and Koszul properties of the homogeneous coordinate ring $K[\\mathcal C]$ of $\\mathcal C$. Whenever $K[\\mathcal C]$ is Cohen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00617","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"}