2019/05/02 by Kazushi Kobayashi, Kobayashi, Kazushi
Mathematics · Physics and Astronomy · #14F05 #14J33 #53D37 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #hep-th #math.DG #msc:14F05 #msc:14J33 #msc:53D37
paper · pdf · doi:10.48550/arxiv.1905.00692
30 pages
openalex publication_date 2019/05/02 · arxiv created 2020/07/05 · arxiv updated 2020/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By the SYZ construction, a mirror pair (X,\checkX) of a complex torus X and a mirror partner \checkX of the complex torus X is described as the special Lagrangian torus fibrations X → B and \checkX → B on the same base space B. Then, by the SYZ transform, we can construct a simple projectively flat bundle on X from each affine Lagrangian multi section of \checkX → B with a unitary local system along it. However, there are ambiguities of the choices of transition functions of it, and this causes difficulties when we try to construct a functor between the symplectic geometric category and the complex geometric category. In this paper, we prove that there exists a bijection between the set of the isomorphism classes of their objects by solving this problem.