Rigidity for Families of Polarized Calabi-Yau Varieties

Details Rigidity for Families of Polarized Calabi-Yau Varieties Rigidity for Families of Polarized Calabi-Yau Varieties

2003-08-05

arxiv.org/abs/math/0308034v4

Mathematics

Algebraic Geometry

38 pages, final version, to appear in J.D.G

Scientific paper

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}.

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