Boundedness of Complements for Log Calabi-Yau Threefolds.

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.