Family Floer cohomology and mirror symmetry
By M. Abouzaid. 2014
61 citations recorded by the source corpus.
Ideas of Fukaya and Kontsevich-Soibelman suggest that one can use Strominger-Yau-Zaslow's geometric approach to mirror symmetry as a torus duality to construct the mirror of a symplectic manifold equipped with a Lagrangian torus fibration as a moduli space of simple objects of the Fukaya category supported on the fibres. In the absence of singular fibres, the construction of the mirror is explained in this framework, and, given a Lagrangian submanifold, a (twisted) coherent sheaf on the mirror is constructed.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a5f800fa9166560caa06e730b5f17f1f1adf1cf9
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces (2012, background): “It is important to note that, even in the absence of superpotentials, the assertion that Y 0 is SYZ mirror to X does not imply that the Fukaya category of X is equivalent to the derived category of Y ; indeed, the example of the Kodaira surface mentioned in [1] shows that there may in general be an ”