The complex and Ricci-flat structure conjecture for the dual torus family
Let be a Calabi--Yau manifold with a special Lagrangian -fibration, and let be the family of dual tori over . The dual torus family conjecture. The family admits complex structures and Ricci-flat Kähler metrics. In particular, it has a nowhere vanishing holomorphic -form. This is presented as the most accessible part of the preceding SYZ compactification conjectures, while the source does not establish it.
References
Primary source
David R. Morrison, “The Geometry Underlying Mirror Symmetry”, arXiv:alg-geom/9608006 (1997).
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