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Suppose that the base field is of characteristic $0$ and the above ideal ${\\frak p}$ is minimally generated by three polynomials. Under the assumption that the homogeneous element $\\xi$ of the minimal degree in ${\\frak p}$ is the negative curve, we determine the minimal degree of an element $\\eta$ such that the pair $\\{ \\xi, \\eta \\}$ satisfies Huneke's criterion in the case where the symbolic Rees rin"},"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":"1705.09865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-27T21:08:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a9e5e2abe0fadeb9d66892b351dcc8859804e3db520526ea8a2b8a130fd339b4","abstract_canon_sha256":"557eeec6fa2a159252ada66e1fdb44cef24e79adc63565a51477f6e353ab6500"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:24.737007Z","signature_b64":"zYJzLsbdq/mOKdS2lGIrC6XNKg9DHVXtjtX+8Q1PR/BOs7mzOxThVUzraRXjXwU/+nBgZQUmhCQ99zpEZWwDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b80baee5afc4a9dafadae27fe5607be9fe3d1b38e17fb98a3ef213b4f9a698f1","last_reissued_at":"2026-05-18T00:43:24.736524Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:24.736524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely generated symbolic Rees rings of space monomial curves having negative curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Kazuhiko Kurano, Koji Nishida","submitted_at":"2017-05-27T21:08:43Z","abstract_excerpt":"In this paper, we shall study finite generation of symbolic Rees rings of the defining ideal ${\\frak p}$ of the space monomial curve $(t^a, t^b, t^c)$ for pairwise coprime integers $a$, $b$, $c$. 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