Abstract
We get a new inequality on the Hodge number \(h^{1,1}(S)\) of fibred algebraic complex surfaces \(S\), which is a generalization of an inequality of Beauville. Our inequality implies the Arakelov type inequalities due to Arakelov, Faltings, Viehweg and Zuo, respectively.
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Acknowledgments
The authors would like to thank Prof. Olivier Debarre, Prof. Ngaiming Mok, Prof. Stefan Müller-Stach and Dr. Xin Lu for useful suggestions and discussions. They thank also the referee for pointing out the misuse of the cohomology classes and forms in the original version of the paper, and for many suggestions to simplify and clarify the proofs. Finally, they express their appreciation to Prof. M. Popa for sending them his interesting joint work on Hodge numbers.
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This work is supported by NSFC, and by the SFB/TR 45 Periods, Moduli Spaces and Arithmetic of Algebraic Varieties of the DFG. The first author and the third author are also supported by the Fundamental Research Funds for the Central Universities.
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Lu, J., Tan, SL., Yu, F. et al. A new inequality on the Hodge number \(h^{1,1}\) of algebraic surfaces. Math. Z. 276, 543–555 (2014). https://doi.org/10.1007/s00209-013-1212-3
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DOI: https://doi.org/10.1007/s00209-013-1212-3