Generalized special Lagrangian torus fibration for Calabi-Yau hypersurfaces in toric varieties I
Wei-Dong Ruan
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 X0. In this paper, we will deal with the region near the smooth top dimensional torus fibres of X0 and its mirror dual situation: the region near the 0-dimensional fibres of X0.
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