Calabi-Yau components in general type hypersurfaces

Details Calabi-Yau components in general type hypersurfaces Calabi-Yau components in general type hypersurfaces

2008-07-11

arxiv.org/abs/0807.1784v1

Mathematics

Algebraic Geometry

Scientific paper

For a one-parameter family of general type hypersurfaces with bases of holomorphic n-forms, we construct open covers using tropical geometry. We show that after normalization, each holomorphic n-form is approximately supported on a unique open component and such a pair approximates a Calabi-Yau hypersurface together with its holomorphic n-form as the parameter becomes large. We also show that the Lagrangian fibers in the fibration constructed by Mikhalkin are asymptotically special Lagrangian. As the holomorphic n-form plays an important role in mirror symmetry for Calabi-Yau manifolds, our results is a step toward understanding mirror symmetry for general type manifolds.

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