Boundedness of elliptic Calabi-Yau threefolds

Abstract

We show that elliptic Calabi--Yau threefolds form a bounded family. We also show that the same result holds for minimal terminal threefolds of Kodaira dimension 2, upon fixing the rate of growth of pluricanonical forms and the degree of a multisection of the Iitaka fibration. Both of these hypotheses are necessary to prove the boundedness of such a family.

arXiv commentFinal version, to appear in J. Eur. Math. Soc. (JEMS)

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Cited by in corpus (3)

• On numerical dimensions of Calabi--Yau varieties
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• Boundedness of stable minimal models with klt singularities