Echoes in genus three of Teichmüller curves in genus two
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917622686154752 |
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| author | Fils, Thomas Le |
| author_facet | Fils, Thomas Le |
| contents | We classify the Teichmüller curves in the moduli space of genus three Riemann surfaces $\mathcal M_3$ that are obtained by a covering construction from a primitive Teichmüller curve in $\mathcal M_2$. We describe the action on homology modulo two of the affine groups of translation surfaces generating these primitive curves. We also classify the $\mathrm{SL}_2(\mathbb Z)$-orbits of square-tiled surfaces in $\mathcal H(2, 2)$ that are a cover of a genus two one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17680 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Echoes in genus three of Teichmüller curves in genus two Fils, Thomas Le Geometric Topology Dynamical Systems We classify the Teichmüller curves in the moduli space of genus three Riemann surfaces $\mathcal M_3$ that are obtained by a covering construction from a primitive Teichmüller curve in $\mathcal M_2$. We describe the action on homology modulo two of the affine groups of translation surfaces generating these primitive curves. We also classify the $\mathrm{SL}_2(\mathbb Z)$-orbits of square-tiled surfaces in $\mathcal H(2, 2)$ that are a cover of a genus two one. |
| title | Echoes in genus three of Teichmüller curves in genus two |
| topic | Geometric Topology Dynamical Systems |
| url | https://arxiv.org/abs/2403.17680 |