论文标题
关于接近Arakelov平等的纤维
On fibrations approaching the Arakelov equality
论文作者
论文摘要
半稳定纤维的Lyapunov指数$ L_F $是基座的Euler特征的Hodge Bundle度的比例。该比率是由Arakelov的不平等从上方界定的。 Sheng-Li Tan表明，对于纤维属$ g \ geq 2 $，从未达到Arakelov平等。我们研究是否有渐近接近Arakelov结合的纤维序列。如果纤维纤维平滑，或非毛elliptic型或具有小的基本属，则答案是否定的。 此外，我们构建了半稳定振动的示例，表明Teichmüller曲线并未达到$ L_F $的最大值可能值。
The sum of Lyapunov exponents $L_f$ of a semi-stable fibration is the ratio of the degree of the Hodge bundle by the Euler characteristic of the base. This ratio is bounded from above by the Arakelov inequality. Sheng-Li Tan showed that for fiber genus $g\geq 2$ the Arakelov equality is never attained. We investigate whether there are sequences of fibrations approaching asymptotically the Arakelov bound. The answer turns out to be no, if the fibration is smooth, or non-hyperelliptic, or has a small base genus. Moreover, we construct examples of semi-stable fibrations showing that Teichmüller curves are not attaining the maximal possible value of $L_f$.
