Joyce, Dominic (2003) Singularities of special Lagrangian fibrations and the SYZ Conjecture. Communications in Analysis and Geometry, 11 . pp. 859-907.
The SYZ Conjecture explains Mirror Symmetry between Calabi-Yau 3-folds , in terms of special Lagrangian fibrations and over the same base , whose fibres are dual 3-tori, except for singular fibres. This paper studies the singularities of special Lagrangian fibrations.
We construct many examples of special Lagrangian fibrations on open subsets of . The simplest are given explicitly, and the rest use analytic existence results for U(1)-invariant special Lagrangian 3-fold in . We then argue that some features of our examples should also hold for generic special Lagrangian fibrations of (almost) Calabi-Yau 3-folds, and draw some conclusions on the SYZ Conjecture.
|Subjects:||D - G > Differential geometry|
|Research Groups:||Geometry Group|
|Deposited By:||Dominic Joyce|
|Deposited On:||07 Jun 2004|
|Last Modified:||20 Jul 2009 14:18|
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