A gerby deformation of complex tori and the homological mirror symmetry
2023 年 46 巻 3 号 p. 291-323
詳細
2023 年 46 巻 3 号 p. 291-323
Let 
be a mirror pair of a complex torus X and its mirror partner 
. This mirror pair is described as the trivial special Lagrangian torus fibrations X → B and → B on the same base space B by SYZ construction. Then, we can associate a holomorphic line bundle 
→ X to a pair 
of a Lagrangian section s of → B and a unitary local system 
along it. In this paper, we first construct the deformation 
of X by a certain flat gerbe 
and its mirror partner 
from the mirror pair , and discuss deformations of objects 
and 
over the deformed mirror pair 
.
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