Rigidity for Families of Polarized Calabi-Yau Varieties

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

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Algebraic Geometry, Complex Variables, Geometric Topology, 14D20

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http://salesiana.dossiersoluciones.com/handle/123456789/68245

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0308034
 http://arxiv.org/abs/math/0308034

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arXiv