On fibrations approaching the Arakelov equality

  • 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.

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Metadaten
Author:Maximilian Bieri
URN:urn:nbn:de:hebis:30:3-637623
DOI:https://doi.org/10.1007/s00209-021-02847-y
ISSN:1432-1823
Parent Title (English):Mathematische Zeitschrift
Publisher:Springer
Place of publication:Berlin ; Heidelberg
Document Type:Article
Language:English
Date of Publication (online):2021/09/01
Date of first Publication:2021/09/01
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2022/03/02
Volume:2021
Issue:online version before inclusion in an issue
Page Number:31
Note:
Open Access funding enabled and organized by Projekt DEAL.
Note:
Research is partially supported by the LOEWE-Schwerpunkt 'Uniformisierte Strukturen in Arithmetik und Geometrie' and by the Friedrich-Ebert-Stiftung.
Note:
Early View: Online Version before inclusion in an issue
HeBIS-PPN:49205326X
Institutes:Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - Namensnennung 4.0