Examples of Special Lagrangian Fibrations
arXiv:math/0012002
Abstract
We explore a number of examples of special Lagrangian fibrations on non-compact Calabi-Yau manifolds invariant under torus actions. These include fibrations on crepant resolutions of canonical toric singularities (already found by Goldstein), proper versions of these fibrations, and fibrations on flat deformations of canonical toric singularities. We do this with an eye towards understanding the global structure and discriminant loci of such fibrations. The paper ends with some speculation, both about local mirror symmetry, and the connections of this work with the work of W.D. Ruan and D. Joyce. In the last section, we discuss the philosophy of the Strominger-Yau-Zaslow conjecture in the light of a number of recent ideas of myself and Wilson, Kontsevich and Soibelman, and Joyce.
29 pages, 10 figures, references added
References in corpus (11)
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- Special Lagrangian Cones
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- Mirror symmetry without corrections
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- Calibrated Fibrations on Complete Manifolds via Torus Action
- Newton polygon and string diagram
- Topological Mirror Symmetry