Boundedness of Complements for Log Calabi–Yau Threefolds
Guodu Chen , Jingjun Han , Qingyuan Xue
Peking Mathematical Journal ›› 2023, Vol. 7 ›› Issue (1) : 1 -33.
Boundedness of Complements for Log Calabi–Yau Threefolds
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 $\mathcal {N}$, such that if a threefold pair $(X/Z\ni z,B)$ has an $\mathbb {R}$-complement which is klt over a neighborhood of z, then it has an n-complement for some $n\in \mathcal {N}$. We also show the boundedness of complements for $\mathbb {R}$-complementary surface pairs.
China post-doctoral(BX2021269)
China post-doctoral grants(2021M702925)
National Key Research and Development Program of China(2020YFA0713200)
Fudan University(JIH1414011Y)
Simons Foundation(814268)
Division of Mathematical Sciences(1801851)
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