{"paper":{"title":"Stable pair invariants on Calabi-Yau threefolds containing P^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yukinobu Toda","submitted_at":"2014-10-14T05:10:39Z","abstract_excerpt":"We relate Pandharipande-Thomas stable pair invariants on Calabi-Yau 3-folds containing the projective plane with those on the derived equivalent orbifolds via wall-crossing method. The difference is described by generalized Donaldson-Thomas invariants counting semistable sheaves on the local projective plane, whose generating series form theta type series for indefinite lattices. Our result also derives non-trivial constraints among stable pair invariants on such Calabi-Yau 3-folds caused by Seidel-Thomas twist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3574","kind":"arxiv","version":1},"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"}