Boundedness of Complements for Log Calabi-Yau Threefolds  

作　　者：Guodu Chen Jingjun Han Qingyuan Xue 

机构地区：[1]Institute for Theoretical Sciences,Westlake University,Hangzhou 310024,Zhejiang,China [2]Shanghai Center for Mathematical Sciences,Fudan University,Shanghai 200438,China [3]Department of Mathematics,The University of Utah,Salt Lake City,UT 84112,USA

出　　处：《Peking Mathematical Journal》2024年第1期1-33,共33页北京数学杂志（英文）

基　　金：supported by the China Post-doctoral Science Foundation(Grant Nos.BX2021269 and 2021M702925);supported by National Key Research and Development Program of China(Grant No.2020YFA0713200);supported by NSF Research Grants(Nos.DMS-1801851 and DMS-1952522);by a grant from the Simons Foundation(Award Number:256202).

摘　　要：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 afinite 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.

关 键 词：COMPLEMENTS Log Calabi-Yau pairs Fano varieties 

分 类 号：O17[理学—数学]