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Generalized special Lagrangian torus fibration for Calabi-Yau hypersurfaces in toric varieties I

Wei-Dong Ruan
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Abstract

In this paper we start the program of constructing generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric variety near the large complex limit, with respect to the restriction of a toric metric on the toric variety to the Calabi-Yau hypersurface. The construction is based on the deformation of the standard toric generalized special Lagrangian torus fibration of the large complex limit $X_0$. In this paper, we will deal with the region near the smooth top dimensional torus fibres of $X_0$ and its mirror dual situation: the region near the 0-dimensional fibres of $X_0$.

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Wei-Dong Ruan. 2003-09-28. Generalized special Lagrangian torus fibration for Calabi-Yau hypersurfaces in toric varieties I. https://arxiv.org/abs/math/0303114

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