Filtration and splitting of the Hodge bundle on the non-varying strata of quadratic differentials

Author:

Dawei Chen, Fei Yu

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Dynamical Systems (math.DS), Geometric Topology (math.GT)

journal:

date:

2023-06-10 16:00:00

Abstract

We describe the Harder--Narasimhan filtration of the Hodge bundle for Teichm\"uller curves in the non-varying strata of quadratic differentials appearing in [CM2]. Moreover, we show that the Hodge bundle on the non-varying 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 Teichm\"uller curves in the non-varying strata and derive new results regarding the asymptotic behavior of Lyapunov exponents.

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