{"paper":{"title":"Donaldson-Thomas theory of $[\\mathbb{C}^2/\\mathbb{Z}_{n+1}]\\times \\mathbb{P}^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Zijun Zhou","submitted_at":"2015-10-03T21:31:24Z","abstract_excerpt":"We study the relative orbifold Donaldson-Thomas theory of $[\\mathbb{C}^2/\\mathbb{Z}_{n+1}]\\times \\mathbb{P}^1$. We establish a correspondence between the DT theory relative to 3 fibers to quantum multiplication by divisors in the Hilbert scheme of points on $[\\mathbb{C}^2/\\mathbb{Z}_{n+1}]$. This determines the whole theory if a further nondegeneracy condition is assumed. The result can also be viewed as a crepant resolution correspondence to the DT theory of $\\mathcal{A}_n\\times \\mathbb{P}^1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00871","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"}