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Rigidity for Families of Polarized Calabi-Yau Varieties

Yi Zhang

math.AGarXiv:math/0308034

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 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, strongly degenerated families (not only for families of Calabi-Yau varieties), families of Calabi-Yau varieties admitting a degeneration with maximal unipotent monodromy.

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