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Geometric structure of exact triangles consisting of projectively flat bundles on higher dimensional complex tori. (arXiv:1705.04007v2 [math.DG] UPDATED)

The mirror dual objects corresponding to affine Lagrangian (multi) sections of a trivial special Lagrangian torus fibration T^{2n}--->T^n are holomorphic vector bundles on a mirror dual complex torus of dimension n via the homological mirror symmetry. In this paper, we construct a one-to-one correspondence between those holomorphic vector bundles and a certain kind of projectively flat bundles explicitly, by using the result of the classification of factors of automorphy of projectively flat bundles on complex tori. Furthermore, we give a geometric interpretation of the exact triangles consisting of projectively flat bundles on complex tori by focusing on the dimension of intersections of the corresponding affine Lagrangian submanifolds.查看全文

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