@article{Chen2024, 
author = {Guodu Chen and Jingjun Han and Qingyuan Xue},
title = {Boundedness of Complements for Log Calabi–Yau Threefolds},
year = {2024},
journal = {Peking Mathematical Journal},
volume = {7},
number = {1},
pages = {1-33},
keywords = {Complements, Log Calabi–Yau pairs, Fano varieties},
url = {https://www.sciopen.com/article/10.1007/s42543-022-00057-x},
doi = {10.1007/s42543-022-00057-x},
abstract = {In this paper, we study the theory of complements, introduced by Shokurov, for Calabi–Yau type varieties with the coefficient set [0, 1]. We show that there exists a finite set of positive integers  N, such that if a threefold pair  (X/Z∋z,B) has an  R-complement which is klt over a neighborhood of z, then it has an n-complement for some  n∈N. We also show the boundedness of complements for  R-complementary surface pairs.}
}