Abstract
By the SYZ construction, a mirror pair (X,Xˇ) of a complex torus X and a mirror partner Xˇ of the complex torus X is described as the special Lagrangian torus fibrations X→B and Xˇ→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 multisection of Xˇ→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.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
