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Boundedness of n-complements for generalized pairs

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Abstract

We show the existence of n-complements for generalized pairs when the coefficients of boundary parts and nef parts belong to a DCC set. As an important step, we show the existence of uniform generalized lc rational polytopes for generalized pairs. As applications, we show the discreteness for generalized minimal log discrepancies for generalized pairs with certain conditions.

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Notes

  1. It is worth mentioning here that the cone theorem for NQC generalized pairs was proved by Hacon and Liu [9] very recently.

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Acknowledgements

This work began when the author visited Jingjun Han at Johns Hopkins University in April of 2019, and the author would like to thank Jingjun Han for suggesting him the problem and also for useful discussions. Part of this work was done while the author visited the MIT Mathematics Department during 2018–2020 supported by China Scholarship Council (File No. 201806010039). The author would like to thank their hospitality. The author would like to thank his advisor Chenyang Xu for constant support and encouragement. The author would also like to thank Jihao Liu and Qingyuan Xue for useful comments. Finally, the author is grateful to the referees for many valuable comments and suggestions.

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  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, China

    Guodu Chen

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Chen, G. Boundedness of n-complements for generalized pairs. European Journal of Mathematics 9, 95 (2023). https://doi.org/10.1007/s40879-023-00693-2

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