{"paper":{"title":"Counting curves on surfaces in Calabi-Yau 3-folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Amin Gholampour, Artan Sheshmani, R. P. Thomas","submitted_at":"2013-08-31T01:12:56Z","abstract_excerpt":"Motivated by S-duality modularity conjectures in string theory, we define new invariants counting a restricted class of 2-dimensional torsion sheaves, enumerating pairs $Z\\subset H$ in a Calabi-Yau threefold X. Here H is a member of a sufficiently positive linear system and Z is a 1-dimensional subscheme of it. The associated sheaf is the ideal sheaf of $Z\\subset H$, pushed forward to X and considered as a certain Joyce-Song pair in the derived category of X. We express these invariants in terms of the MNOP invariants of X."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0051","kind":"arxiv","version":3},"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"}