Calabi-Yau varieties and Fano varieties are building blocks of varieties in the sense of birational geometry. They are expected to satisfying certain finiteness. Recent progress on BAB Conjecture shows that certain Fano varieties form a bounded family. We are looking for the analogue for Calabi-Yau varieties. We only consider rationally connected Calabi-Yau varieties with klt singularities, which are those Calabi-Yau varieties behaving most like Fano. This is a follow-up of my talk in 2017/12/14. Last time I talked about the birational boundedness of rationally connected klt Calabi-Yau 3-folds. I will show that if we add some reasonable assumption, then we can get a stronger boundedness result for rationally connected klt Calabi-Yau 3-folds. It is also related to Shokurov’s conjecture on minimal log discrepancies.

This is a joint work with W. Chen, G. Di Cerbo, J. Han, and R. Svaldi.

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