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

TL;DR

This paper analyzes the structure of the Hodge bundle on non-varying strata of quadratic differentials, revealing its filtration and splitting properties, and computes Lyapunov exponents for related Teichmüller curves.

Contribution

It describes the Harder--Narasimhan filtration and splitting of the Hodge bundle in non-varying strata, providing explicit Lyapunov exponent calculations.

Findings

Hodge bundle admits a Harder--Narasimhan filtration in these strata.

The Hodge bundle can split as a direct sum of line bundles.

All Lyapunov exponents for algebraically primitive Teichmüller curves are determined.

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.