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Deformations of elliptic Calabi-Yau manifolds

Author(s): Kollar, Janos

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Abstract: We investigate deformations and characterizations of elliptic Calabi-Yau varieties, building on earlier works of Wilson and Oguiso. We show that if the second cohomology of the structure sheaf vanishes, then every deformation is again elliptic. More generally, all non-elliptic deformations derive from abelian varieties or K3 surfaces. We also give a numerical characterization of elliptic Calabi-Yau varieties under some positivity assumptions on the second Todd class. These results lead to a series of conjectures on fibered Calabi-Yau varieties.
Publication Date: 2015
Electronic Publication Date: 2015
Citation: Kollar, J. (2015). Deformations of elliptic Calabi-Yau manifolds. Recent Advances in Algebraic Geometry, 417 (254 - 290
ISSN: 0076-0552
Pages: 254 - 290
Type of Material: Journal Article
Journal/Proceeding Title: Recent Advances in Algebraic Geometry
Version: Author's manuscript

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