{"paper":{"title":"Quantum Singularity Theory for A_{r-1} and r-Spin Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.DG"],"primary_cat":"math.AG","authors_text":"Huijun Fan, Tyler J. Jarvis, Yongbin Ruan","submitted_at":"2010-12-01T00:01:29Z","abstract_excerpt":"We give a review of the quantum singularity theory of Fan-Jarvis-Ruan and the r-spin theory of Jarvis-Kimura-Vaintrob and describe the work of Abramovich-Jarvis showing that for the singularity A_{r-1} = x^r the stack of A_{r-1}-curves of is canonically isomorphic to the stack of r-spin curves. We prove that the A_{r-1}-theory satisfies all the axioms of Jarvis-Kimura-Vaintrob for an r-spin virtual class. Therefore, the results of Lee, Faber-Shadrin-Zovonkine, and Givental all apply to the A_{r-1}-theory. In particular, this shows that the Witten Integrable Hierarchies Conjecture is true for t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0066","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"}