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Chern number inequalities of deformed Hermitian-Yang-Mills metrics on four dimensional Kähler manifolds

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Abstract

In this paper, we give an affirmative answer to a conjecture of Collins-Yau [8]. We investigate the Chern number inequalities on 4-dimensional Kähler manifolds admitting the deformed Hermitian-Yang-Mills metrics under the assumption \({{\hat{\theta }}}\in (\pi ,2\pi )\).

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Acknowledgements

The authors would like to thank T. Collins and J. Xiao for some helpful discussions. The research is partially supported by NSFC 11721101. The first author is supported by National Key R &D Program of China 2022YFA1005400 and NFSC No.12031017 and the second author is supported by NSFC No.12001532.

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Authors and Affiliations

  1. Math Department of Tsinghua University, Beijing, 100084, China

    Xiaoli Han

  2. Department of Mathematics, Renmin University of China, Beijing, 100872, China

    Xishen Jin

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  1. Xiaoli Han
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Correspondence to Xishen Jin.

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Han, X., Jin, X. Chern number inequalities of deformed Hermitian-Yang-Mills metrics on four dimensional Kähler manifolds. manuscripta math. (2024). https://doi.org/10.1007/s00229-023-01531-1

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