The Mathematical Institute, University of Oxford, Eprints Archive

Singularities of special Lagrangian fibrations and the SYZ Conjecture

Joyce, Dominic (2003) Singularities of special Lagrangian fibrations and the SYZ Conjecture. Communications in Analysis and Geometry, 11 . pp. 859-907.

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Abstract

The SYZ Conjecture explains Mirror Symmetry between Calabi-Yau 3-folds $M$, $\hat{M}$ in terms of special Lagrangian fibrations $f : M \rightarrow B$ and $\hat{f} : \hat{M} \rightarrow B$ over the same base $B$, 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 $\mathbb{C}^3$. The simplest are given explicitly, and the rest use analytic existence results for U(1)-invariant special Lagrangian 3-fold in $\mathbb{C}^3$. 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.

Item Type:Article
Subjects:D - G > Differential geometry
Research Groups:Geometry Group
ID Code:81
Deposited By:Dominic Joyce
Deposited On:07 Jun 2004
Last Modified:20 Jul 2009 14:18

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