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When $d=2$ and $I$ is saturated, we give an algorithm for obtaining this resolution that involves the computation of a minimal Gr\\\"obner basis of $I$ with"},"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":"1704.01777","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-04-06T10:42:53Z","cross_cats_sorted":["math.AG","math.CO"],"title_canon_sha256":"fec68d91df7071630ea91dc980c78560b32fe40e0f199750bcf4bbe0964d8ff9","abstract_canon_sha256":"ea4be79a027463613c04fa5cd582cf341b752e42f9541f22606e15155627d0b4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:25.575092Z","signature_b64":"QhmmgPCuRwt/4fgKrB4Ym6yxY3LWf6Y2+Tri/uGrrk/LeHPkrSEfzegkVKfjNWZcHbK0PWoItdWLvhu8i1UABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5082244fab2cad5542907d44a1298e1501a5c00830e1f2c350d1ba9255969fa","last_reissued_at":"2026-05-18T00:45:25.574725Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:25.574725Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noether resolutions in dimension $2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AC","authors_text":"Eva Garc\\'ia-Llorente, Ignacio Garc\\'ia-Marco, Isabel Bermejo, Marcel Morales","submitted_at":"2017-04-06T10:42:53Z","abstract_excerpt":"Let $R:= K[x_1,\\ldots,x_{n}]$ be a polynomial ring over an infinite field $K$, and let $I \\subset R$ be a homogeneous ideal with respect to a weight vector $\\omega = (\\omega_1,\\ldots,\\omega_n) \\in (\\mathbb{Z}^+)^n$ such that $\\dim(R/I) = d$. 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