Abstract
Let f : X → B be a generic ordinary proper fibration over a complete curve in positive characteristics, we prove that the dual of higher direct image sheaf \(R^1f_*\mathcal{O}_X\) is nef. As a corollary, we show that f*ωS/B is nef, if f : S → B is a fibration from a surface to a curve with generic ordinary fibres.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11231003 and 11321101). The authors thank Professor Xiaotao Sun for useful suggestions and encouragements. The authors are very grateful to the referees for valuable comments and suggestions.
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Chen, Y., Gu, Y. Semipositivity of generic ordinary fibration over a curve. Sci. China Math. 61, 1749–1758 (2018). https://doi.org/10.1007/s11425-017-9104-7
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DOI: https://doi.org/10.1007/s11425-017-9104-7