2013/08/05 by Xiaowen Hu, Hu, Xiaowen
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Ancestor #Artificial intelligence #Black Holes and Theoretical Physics #Combinatorics #Computer science #Conjecture #FOS: Mathematics #Field (mathematics) #Geography #Geometry #Gravitational singularity #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum #Quantum mechanics #Resolution (logic) #Surface (topology) #math.AG
paper · pdf · doi:10.48550/arxiv.1308.0997
Typos and small mistakes corrected
openalex publication_date 2013/08/05 · arxiv created 2013/12/15 · arxiv updated 2013/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We state a version of the crepant resolution conjecture for total ancestor potentials for surface singularities, and reduce the conjecture to the quantum McKay correspondence conjecture of J.Bryan and A.Gholampour and a vanishing conjecture for Hurwitz-Hodge integrals. In particular, for singularities of type A, we prove the conjecture. We also suggest an approach towards a proof for the general cases by Teleman's reconstruction theorem for semisimple cohomological field theories.