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Original Article | Open Access

Boundedness of Complements for Log Calabi–Yau Threefolds

Institute for Theoretical Sciences, Westlake University, Hangzhou 310024, Zhejiang, China
Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200438, China
Department of Mathematics, The University of Utah, Salt Lake City, UT 84112, USA
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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.

Keywords

Fano varietiesComplementsLog Calabi–Yau pairs
Peking Mathematical Journal
Volume 7 Issue 1,
March 2024
Pages 1-33
DOI: 10.1007/s42543-022-00057-x
Cite this article:
Chen, G., Han, J. & Xue, Q. Boundedness of Complements for Log Calabi–Yau Threefolds. Peking Math J 7, 1-33 (2024). https://doi.org/10.1007/s42543-022-00057-x

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Received: 16 July 2022
Revised: 03 November 2022
Accepted: 17 November 2022
Published: 07 February 2023
© The Author(s) 2023

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