This article is cited in 14 papers

Birational boundedness of rationally connected Calabi-Yau 3-folds

Weichung Chen^a, Gabriele Di Cerbo^b, Jingjun Han^c, Chen Jiang^d, Roberto Svaldi<sup>e

a</sup> Graduate School of Mathematical Sciences, the University of Tokyo, Tokyo, Japan
^b Department of Mathematics, Princeton University, Princeton, NJ, USA
^c Department of Mathematics, Johns Hopkins University, Baltimore, MD, USA
^d Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China
^e EPFL, Lausanne, Switzerland

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.

Language: English

 English version: DOI: 10.1016/j.aim.2020.107541

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