TY  - JOUR
A1  - Bieri, Maximilian
T1  - On fibrations approaching the Arakelov equality
T2  - Mathematische Zeitschrift
N2  - The sum of Lyapunov exponents Lf 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≥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 Lf.
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63762
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-637623
SN  - 1432-1823
N1  - Open Access funding enabled and organized by Projekt DEAL.
N1  - Research is partially supported by the LOEWE-Schwerpunkt 'Uniformisierte Strukturen in Arithmetik und Geometrie' and by the Friedrich-Ebert-Stiftung.
N1  - Early View: Online Version before inclusion in an issue
VL  - 2021
IS  - online version before inclusion in an issue
PB  - Springer
CY  - Berlin ; Heidelberg
ER  -