Weierstrass filtration on Teichmüller curves and Lyapunov exponents: Upper bounds

We get an upper bound of the slope of each graded quotient for the Harder-Narasimhan filtration of the Hodge bundle of a Teichmüller curve. As an application, we show that the sum of Lyapunov exponents of a Teichmüller curve does not exceed ${(g+1)}/{2}$, with equality reached if and only if the curve lies in the hyperelliptic locus induced from $\mathcal{Q}(2k_1,...,2k_n,-1^{2g+2})$ or it is a special Teichmüller curve in $Ω\mathcal{M}_g(1^{2g-2})$. It also gives an unified interpretation for many known results about the special partial sums of Lyapunov exponents on Teichmüller curves.

No reviews yet.

No comments yet.