Special curves in modular surfaces
We show that geodesics in $\mathbf {H}$ attached to a maximal split torus or a real quadratic torus in $GL_{2, \mathbf {Q}}$ are the only irreducible algebraic curves in $\mathbf {H}$ whose image in $\mathbf {R}^2$ via the j-invariant is contained in an algebraic curve.
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| Veröffentlicht in: | Canadian mathematical bulletin 2023-03, Vol.66 (1), p.1-18 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We show that geodesics in
$\mathbf {H}$
attached to a maximal split torus or a real quadratic torus in
$GL_{2, \mathbf {Q}}$
are the only irreducible algebraic curves in
$\mathbf {H}$
whose image in
$\mathbf {R}^2$
via the j-invariant is contained in an algebraic curve. |
|---|---|
| ISSN: | 0008-4395 1496-4287 |
| DOI: | 10.4153/S0008439521000941 |