Special curves in modular surfaces

Special curves in modular surfaces

We show that geodesics in the upper half-plane attached to a maximal split torus or a real quadratic torus in \(GL_{2, \mathbf{Q}}\) are the only irreducible algebraic curves whose image via the \(j\)-invariant is contained in an algebraic curve.

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Veröffentlicht in:arXiv.org 2021-05
1. Verfasser: Tamiozzo, Matteo
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Geodesy
Toruses
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Zusammenfassung:We show that geodesics in the upper half-plane attached to a maximal split torus or a real quadratic torus in \(GL_{2, \mathbf{Q}}\) are the only irreducible algebraic curves whose image via the \(j\)-invariant is contained in an algebraic curve.
ISSN:2331-8422