Rigidity for Families of Polarized Calabi-Yau Varieties
Algebraic Geometry
2007-05-23 v4 Complex Variables
Geometric Topology
Abstract
In this paper, we study the analogue of the Shafarevich conjecture for polarized Calabi-Yau varieties. We use variations of Hodge structures and Higgs bundles to establish a criterion for the {\it rigidity} of families. We then apply the criterion to obtain that some important and typical families of Calabi-Yau varieties are rigid, for examples., Lefschetz pencils of Calabi-Yau varieties, {\it strongly degenerated} families (not only for families of Calabi-Yau varieties), families of Calabi-Yau varieties admitting a degeneration with {\it maximal unipotent monodromy}.
Keywords
Cite
@article{arxiv.math/0308034,
title = {Rigidity for Families of Polarized Calabi-Yau Varieties},
author = {Yi Zhang},
journal= {arXiv preprint arXiv:math/0308034},
year = {2007}
}
Comments
38 pages, final version, to appear in J.D.G