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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.00617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-12-02T09:06:41Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"fd9e34516213f90432f0acabe11c76315f571933ce7b956c1e4d791998b1cce5","abstract_canon_sha256":"01f336e446abaafcf58eb1319e0b6cfdb823714965f7f2942c8cfea8bee71f60"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:50.686902Z","signature_b64":"+6E+ZA5i/O7B1xGP/5shnAjCEYEb0ks1wY8UKnWOJtAxEB/KmV4fnOUaTf3HzrbOEfIvArrtG3Dex1uSOCg+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0884bc6a0af5ca5edaf8c228866a59189cc495bac933fc30b17ffd15ac5925d","last_reissued_at":"2026-05-18T00:52:50.686212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:50.686212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathcal C$. 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