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Family of curves with large unitary summand in the Hodge bundle

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Abstract

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.

Keywords

Family Unitary bundle Xiao’s conjecture 

Mathematics Subject Classification

14D06 14H10 14D99 

Notes

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Shanghai Key Laboratory of PMMPEast China Normal UniversityShanghaiPeople’s Republic of China

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