2012/03/27 by Antoine Douai, Douai, Antoine
Mathematics · #14N35 #32S40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1203.5920
openalex publication_date 2012/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems. We focuse on the logarithmic and non-resonant case, which describes the geometric situation. We show that quantum differential systems provide a good framework in order to generalize the construction of the rational structure on the A-side given by Katzarkov, Kontsevitch and Pantev for the projective spaces. As an application, we compute the rational structure obtained in this way on the orbifold cohomology of weighted projective spaces. As an example we also calculate, using quantum differential systems, a mirror partner of the Hirzebruch surface F2.