Open Access
Oct 2004 Rigidity for Families of Polarized Calabi–Yau Varieties
Yi Zhang
J. Differential Geom. 68(2): 185-222 (Oct 2004). DOI: 10.4310/jdg/1115669511


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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Yi Zhang. "Rigidity for Families of Polarized Calabi–Yau Varieties." J. Differential Geom. 68 (2) 185 - 222, Oct 2004.


Published: Oct 2004
First available in Project Euclid: 9 May 2005

zbMATH: 1081.14055
MathSciNet: MR2144247
Digital Object Identifier: 10.4310/jdg/1115669511

Rights: Copyright © 2004 Lehigh University

Vol.68 • No. 2 • Oct 2004
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