# Homological mirror symmetry and torus fibrations

@inproceedings{Kontsevich2000HomologicalMS, title={Homological mirror symmetry and torus fibrations}, author={Maxim Kontsevich and Yan S. Soibelman}, year={2000} }

In this paper we discuss two major conjectures in Mirror Symmetry: Strominger-Yau-Zaslow conjecture about torus fibrations, and the homological mirror conjecture (about an equivalence of the Fukaya category of a Calabi-Yau manifold and the derived category of coherent sheaves on the dual Calabi-Yau manifold). Our point of view on the origin of torus fibrations is based on the standard differential-geometric picture of collapsing Riemannian manifolds as well as analogous considerations for…

## 541 Citations

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Motivated by the picture of mirror symmetry suggested by Strominger, Yau and Zaslow, we made a conjecture concerning the Gromov-Hausdorff limits of Calabi-Yau n-folds (with Ricci-flat K\"ahler…

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