On fibrations approaching the Arakelov equality

Author:

Bieri Maximilian

Abstract

AbstractThe sum of Lyapunov exponents $$L_f$$ 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 $$g\ge 2$$ g 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 $$L_f$$ L f .

Funder

Johann Wolfgang Goethe-Universität, Frankfurt am Main

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A remark on a conjecture of Tan;Monatshefte für Mathematik;2023-03-18

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