Deformations of elliptic calabi-yau manifolds

J. Kollár

doi:10.1007/97811074160000.15

Deformations of elliptic calabi-yau manifolds

J. Kollár

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

6 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.

Original language	English (US)
Title of host publication	Recent Advances in Algebraic Geometry
Subtitle of host publication	A Volume in Honor of Rob Lazarsfeld's 60th Birthday
Publisher	Cambridge University Press
Pages	254-290
Number of pages	37
ISBN (Electronic)	9781107416000
ISBN (Print)	9781107647558
DOIs	https://doi.org/10.1007/97811074160000.15
State	Published - Jan 1 2015

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/97811074160000.15

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Deformations of elliptic calabi-yau manifolds

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