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Singularities of special Lagrangian fibrations and the SYZ Conjecture

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...

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Publication date:
2003-01-01
URN:
uuid:828059f4-73b8-4694-84bf-63cc71627593
Local pid:
oai:eprints.maths.ox.ac.uk:81

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