Birational boundedness of rationally connected Calabi-Yau 3-folds

Abstract

We prove that rationally connected Calabi--Yau 3-folds with kawamata log terminal (klt) singularities form a birationally bounded family, or more generally, rationally connected $3$-folds of $\epsilon$-CY type form a birationally bounded family for $\epsilon >0$. Moreover, we show that the set of $\epsilon$-lc log Calabi--Yau pairs $(X,B)$ with coefficients of $B$ bounded away from zero is log bounded modulo flops. As a consequence, we deduce that rationally connected klt Calabi--Yau $3$-folds with mld bounded away from $1$ are bounded modulo flops.

arXiv comment28 pages, to appear in Advances in Mathematics

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Cited by in corpus (13)

• ACC for minimal log discrepancies of exceptional singularities
• Log Calabi-Yau fibrations
• Invariance of Plurigenera and boundedness for Generalized Pairs
• Boundedness of elliptic Calabi-Yau varieties with a rational section
• A gap theorem for minimal log discrepancies of non-canonical singularities in dimension three
• Birational boundedness of low dimensional elliptic Calabi-Yau varieties with a section
• Boundedness of $(\epsilon ,n)$-Complements for Surfaces
• On the boundedness of $n$-folds with $\kappa (X)=n-1$
• Boundedness of log pluricanonical representations of log Calabi-Yau pairs in dimension 2
• Effective birationality for sub-pairs with real coefficients
• On termination of flips and exceptionally non-canonical singularities
• On birational boundedness of some Calabi-Yau hypersurfaces
• On smooth Calabi-Yau threefolds of Picard number two