Geodesic
Special curves in modular surfaces
Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 1-18

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DOI

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.
DOI : 10.4153/S0008439521000941
Mots-clés : Geodesics, modular curve, j-invariant, functional transcendence 
Tamiozzo, Matteo. Special curves in modular surfaces. Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 1-18. doi: 10.4153/S0008439521000941
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