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29 March 2024
 
  » arxiv » math.AG/0308034

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Rigidity for Families of Polarized Calabi-Yau Varieties
Yi Zhang ;
Date 5 Aug 2003
Subject Algebraic Geometry; Complex Variables; Geometric Topology MSC-class: 14D20 | math.AG math.CV math.GT
AbstractIn 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}.
Source arXiv, math.AG/0308034
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