Deformations of elliptic calabi-yau manifolds

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2 Scopus citations

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. To Robert Lazarsfeld on the occasion of his sixtieth birthday

Original languageEnglish (US)
Title of host publicationRecent Advances in Algebraic Geometry
Subtitle of host publicationA Volume in Honor of Rob Lazarsfeld's 60th Birthday
PublisherCambridge University Press
Pages254-290
Number of pages37
ISBN (Electronic)9781107416000
ISBN (Print)9781107647558
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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    Kollar, J. (2015). Deformations of elliptic calabi-yau manifolds. In Recent Advances in Algebraic Geometry: A Volume in Honor of Rob Lazarsfeld's 60th Birthday (pp. 254-290). Cambridge University Press. https://doi.org/10.1007/97811074160000.15