Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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Filtration and splitting of the Hodge bundle on the nonvarying strata of quadratic differentials
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by Dawei Chen and Fei Yu;
Trans. Amer. Math. Soc. 378 (2025), 5057-5086
DOI: https://doi.org/10.1090/tran/9416
Published electronically: March 19, 2025

Abstract:

We describe the Harder–Narasimhan filtration of the Hodge bundle for Teichmüller curves in the nonvarying strata of quadratic differentials appearing in the work of Dawei Chen and Martin Möller [Ann. Sci. ’Ec. Norm. Sup’er. (4) 47 (2014), pp. 309–369]. Moreover, we show that the Hodge bundle on the nonvarying strata away from the irregular components can split as a direct sum of line bundles. As applications, we determine all individual Lyapunov exponents of algebraically primitive Teichmüller curves in the nonvarying strata and derive new results regarding the asymptotic behavior of Lyapunov exponents.
References
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Bibliographic Information
  • Dawei Chen
  • Affiliation: Department of Mathematics, Boston College, Chestnut Hill, Massachusetts 02467
  • MR Author ID: 848983
  • ORCID: 0000-0002-3926-2636
  • Email: dawei.chen@bc.edu
  • Fei Yu
  • Affiliation: School of Mathematical Sciences, Zhejiang University, Hangzhou, China
  • Email: yufei@zju.edu.cn
  • Received by editor(s): June 29, 2023
  • Received by editor(s) in revised form: January 15, 2025
  • Published electronically: March 19, 2025
  • Additional Notes: Research of the first author was supported by National Science Foundation Grants DMS-2301030, DMS-2001040, Simons Travel Support for Mathematicians, and Simons Fellowship.
    Research of the second author was supported by the National Natural Science Foundation of China under Grant No. 11871422 and the Fundamental Research Funds for the Central Universities 107101*17221022301(2021FZZX001-01).
  • © Copyright 2025 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 378 (2025), 5057-5086
  • MSC (2020): Primary 14H10, 32G15
  • DOI: https://doi.org/10.1090/tran/9416