Abstract
In this paper, we establish a relationship between fractional Dehn twist coefficients of Riemann surface automorphisms and modular invariants of holomorphic families of algebraic curves. Specially, we give a characterization of pseudo-periodic maps with nontrivial fractional Dehn twist coefficients. We also obtain some uniform lower bounds of non-zero fractional Dehn twist coefficients.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 11601504) and Fundamental Research Funds of the Central Universities (Grant No. DUT18RC(4)065). The author thanks Professors Shengli Tan and Jun Lu for their interesting and fruitful discussions, and thanks Professors Youlin Li, Xiaoming Du and Yumin Zhong for their discussions on Dehn twist. The author is very grateful to Professors Tadashi Ashikaga and Yukio Matsumoto for helpful comments on pseudo-periodic maps. The author also thanks the referees for pointing out mistakes.
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Liu, XL. Fractional Dehn twists and modular invariants. Sci. China Math. 64, 1735–1744 (2021). https://doi.org/10.1007/s11425-019-1716-4
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DOI: https://doi.org/10.1007/s11425-019-1716-4