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Boundedness of elliptic Calabi-Yau threefolds
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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.
Forward citations
Cited by 2 Pith papers
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A Picard rank bound for base surfaces of elliptic Calabi-Yau 3-folds
The Picard rank of any rational base surface of an elliptic Calabi-Yau 3-fold (with the relevant 1/6-lc condition) is at most 568.
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Explicit Bounds on the Spectrum of 6d N=(1,0) Supergravity
A new geometric strategy using 1/6-log-canonical pairs and P1 fibrations is proposed to bound the tensor spectrum of 6d N=(1,0) supergravity, with an announced bound T ≤ 567 whose proof is deferred to a companion paper.
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