Variations of Hodge structures of a Teichmueller curve
| dc.creator | Moeller, Martin | |
| dc.date | 2004-01-22 | |
| dc.date | 2005-07-19 | |
| dc.date.accessioned | 2026-07-07T05:04:45Z | |
| dc.date.available | 2026-07-07T05:04:45Z | |
| dc.description | Teichmueller curves are geodesic discs in Teichmueller space that project to an algebraic curve in the moduli space $M_g$. We show that for all $g \geq 2$ Teichmueller curves map to the locus of real multiplication in the moduli space of abelian varieties. Remark that McMullen has shown that precisely for $g=2$ the locus of real multiplication is stable under the $\SL_2(\RR)$-action on the tautological bundle $Ω\M_g$. We also show that Teichmueller curves are defined over number fields and we provide a completely algebraic description of Teichmueller curves in terms of Higgs bundles. As a consequence we show that the absolute Galois group acts on the set of Teichmueller curves. | |
| dc.identifier | https://arxiv.org/abs/math/0401290 | |
| dc.identifier | http://arxiv.org/abs/math/0401290 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69925 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32G15, 32G20, 14G35 | |
| dc.title | Variations of Hodge structures of a Teichmueller curve | |
| dc.type | text |