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Family of curves with large unitary summand in the Hodge bundle

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In this note, we construct non-isotrivial families of curves of genus \(g\ge 2\), where the rank of the unitary summand contained in the Hodge bundle can be as large as \((2g+1)/3\), and hence disprove Xiao’s conjecture for the unitary rank.

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Acknowledgements

The author would like to thank K. Zuo for many useful discussion. He is also grateful to L. Stoppino and V. González-Alonso for a careful reading of a draft of this note.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, No. 500 Dongchuan Road, Shanghai, 200241, People’s Republic of China

    Xin Lu

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  1. Xin Lu
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Correspondence to Xin Lu.

Additional information

This work is supported by the Recruitment Program for Young Professionals, and also partially by SFB/Transregio 45 Periods, Moduli Spaces and Arithmetic of Algebraic Varieties of Deutsche Forschungsgemeinschaft (DFG)

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Lu, X. Family of curves with large unitary summand in the Hodge bundle. Math. Z. 291, 1381–1387 (2019). https://doi.org/10.1007/s00209-018-2181-3

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  • DOI: https://doi.org/10.1007/s00209-018-2181-3

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