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The partial C0-estimate along a general continuity path and applications

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Abstract

We establish a new partial C0-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted (1, 1)-form on Fano manifolds. As an application, this estimate enables us to show the reductivity of the automorphism group of the limit space, which leads to a new proof of the Yau-Tian-Donaldson conjecture.

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Acknowledgements

The second author was supported by Le Centre de recherche en géométrie et topologie Fellowship during the visit to Institut des sciences mathématiques of Université du Québec à Montréal. The authors express their sincere acknowledgement to Professor Gang Tian and Xiaohua Zhu for suggesting this problem and a lot of discussions and encouragements. They also want to thank Chi Li, Zhenlei Zhang and Feng Wang for their beneficial advice on this work. The second author wants to thank Institut des sciences mathématiques of Université du Québec à Montréal, McGill University and Beijing International Center for Mathematical Research for their hospitality during this work. Finally, the authors thank the referees for their beneficial advice on the work.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Ke Feng

  2. School of Mathematical Sciences, Beihang University, Beijing, 100191, China

    Liangming Shen

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  1. Ke Feng
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  2. Liangming Shen
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Correspondence to Liangming Shen.

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Feng, K., Shen, L. The partial C0-estimate along a general continuity path and applications. Sci. China Math. 64, 2495–2520 (2021). https://doi.org/10.1007/s11425-019-1656-2

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  • DOI: https://doi.org/10.1007/s11425-019-1656-2

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