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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| Author: | Maximilian Bieri |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-637693 |
| 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: | 2022/04/27 |
| Volume: | 300 |
| Issue: | 2 |
| Page Number: | 31 |
| First Page: | 1873 |
| Last Page: | 1903 |
| Note: | Open Access funding enabled and organized by Projekt DEAL. |
| HeBIS-PPN: | 494735368 |
| Institutes: | Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - Namensnennung 4.0 |
