Filtration and splitting of the Hodge bundle on the nonvarying strata of quadratic differentials

Chen, Dawei; Yu, Fei

doi:10.1090/tran/9416

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

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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.

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Filtration and splitting of the Hodge bundle on the nonvarying strata of quadratic differentials
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Abstract: