Calabi-Yau components in general type hypersurfaces
Algebraic Geometry
2008-07-14 v1 Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.0807.1784,
title = {Calabi-Yau components in general type hypersurfaces},
author = {Naichung Conan Leung and Tom Y. H. Wan},
journal= {arXiv preprint arXiv:0807.1784},
year = {2008}
}