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 $\hat{I}\mu$-CY type form a birationally bounded family for $\hat{I}\mu >0$. Moreover, we show that the set of $\hat{I}\mu$-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.

28 pages, to appear in Advances in Mathematics