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.
Boundedness of elliptic Calabi-Yau threefolds / S. Filipazzi, C.D. Hacon, R. Svaldi. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - 27:9(2025), pp. 3583-3650. [10.4171/JEMS/1467]
Boundedness of elliptic Calabi-Yau threefolds
R. SvaldiUltimo
2025
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.
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