{"paper":{"title":"The Donaldson-Thomas theory of $K3\\times E$ via the topological vertex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Jim Bryan","submitted_at":"2015-04-11T22:28:22Z","abstract_excerpt":"Oberdieck and Pandharipande conjectured that the curve counting invariants of $S\\times E$, the product of a $K3$ surface and an elliptic curve, is given by minus the reciprocal of the Igusa cusp form of weight 10. For a fixed primitive curve class in $S$ of square $2h-2$, their conjecture predicts that the corresponding partition functions are given by meromorphic Jacobi forms of weight $-10$ and index $h-1$. We calculate the partition functions for primitive classes of square -2 and of square 0.\n  Our computation uses reduced Donaldson-Thomas invariants which are defined as the Behrend functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02920","kind":"arxiv","version":2},"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"}