Weierstrass filtration on Teichmüller curves and Lyapunov exponents: Upper bounds

الأصل · EN

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 Q(2k₁,...,2kₙ,-1²ᵍ⁺²) or it is a special Teichmüller curve in ΩMg(1²ᵍ⁻²). It also gives an unified interpretation for many known results about the special partial sums of Lyapunov exponents on Teichmüller curves.