{"@context":"https://schema.org","@type":"CreativeWork","@id":"https://froggit.ai/public/capsules/1a9ad183-ca2c-410f-8f45-2974b3589f66","identifier":"1a9ad183-ca2c-410f-8f45-2974b3589f66","url":"https://froggit.ai/public/capsules/1a9ad183-ca2c-410f-8f45-2974b3589f66","name":"ArxivPaper: The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds","text":"# ArxivPaper: The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds\n\nLet $X$ be a projective complex 3-manifold. An effective curve class $β\\in H_2(X,\\mathbb Z)$ is called positive if $c_1(X)\\cdotβ>0$, and superpositive if all the effective summands of $β$ are positive. If $X$ is Fano then all curve classes are superpositive. In arXiv:2111.04694 the second author developed a theory of enumerative invariants in abelian categories and wall-crossing formulae. We use this theory to prove conjectures by Pandharipande and Thomas on the rationality and poles of generating functions of Pandharipande-Thomas invariants of $X$ with descendent insertions, for superpositive curve classes.\n\n## Properties\n| Property | Value |\n|----------|-------|\n| arxiv_id | 2604.05664v1 |\n| categories | ['math.AG'] |\n| doi | 10.48550/arXiv.2604.05664 |\n| primary_category | math.AG |\n| published | 2026-04-07T10:05:56Z |\n| source | arxiv |\n| summary | Let $X$ be a projective complex 3-manifold. An effective curve class $β\\in H_2(X,\\mathbb Z)$ is called positive if $c_1(X)\\cdotβ>0$, and superpositive if all the effective summands of $β$ are positive |\n| title | The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds |\n| updated | 2026-04-07T10:05:56Z |\n\n## Source\n- Category: scholarly\n- Confidence: 0.9\n- Nodes included: 1\n\n## Source Basis\n- Source basis: Forge Neo4j `ArxivPaper` nodes in the `scholarly` category.\n- Source reference: forge://neo4j/scholarly/ArxivPaper\n- Source node count: 1\n- Source grouping: primary_category=math.AG\n- Source element IDs: 4:2b225304-0b3a-4c6c-a526-0d18559d1d1f:26486","keywords":["arxivpaper","scholarly","auto-curated","math.ag"],"about":[],"citation":["forge://neo4j/scholarly/ArxivPaper","neo4j:ArxivPaper:4:2b225304-0b3a-4c6c-a526-0d18559d1d1f:26486","doi:10.48550/arXiv.2604.05664","arxiv:2111.04694","ArxivPaper"],"isPartOf":{"@type":"Dataset","name":"Froggit.ai Knowledge Graph","url":"https://froggit.ai"},"publisher":{"@type":"Organization","name":"Froggit.ai","url":"https://froggit.ai"},"dateCreated":"2026-06-30T08:08:36.703698Z","dateModified":"2026-06-30T15:18:59.462000Z","isBasedOn":"forge://neo4j/scholarly/ArxivPaper","additionalProperty":[{"@type":"PropertyValue","name":"trust_level","value":80},{"@type":"PropertyValue","name":"verification_status","value":"sources_checked"},{"@type":"PropertyValue","name":"provenance_status","value":"valid"},{"@type":"PropertyValue","name":"evidence_level","value":"primary_source"},{"@type":"PropertyValue","name":"content_hash","value":"83f5d16c1d22c4f75b69b0b0906f7bc96b8ae426f78f19be5f20aa56dfe0ea59"}]}