Abstract
Let (Xn,Xˇn) be a mirror pair of an n-dimensional complex torus Xn and its mirror partner Xˇn. Then, by SYZ transform, we can construct a holomorphic line bundle with an integrable connection from each pair of a Lagrangian section of Xˇn→Rn/Zn and a unitary local system along it, and those holomorphic line bundles with integrable connections form a dg-category DGXn. In this paper, we focus on a certain B-field transform of the generalized complex structure induced from the complex structure on Xn, and interpret it as the deformation XGn of Xn by a flat gerbe G. Moreover, we construct the deformation of DGXn associated to the deformation from Xn to XGn, and also discuss the homological mirror symmetry between XGn and its mirror partner on the object level.
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