Real multiplication through explicit correspondences

DOI10.1112/S1461157016000188zbMath1367.14012arXiv1602.01924OpenAlexW2255575672MaRDI QIDQ2970997

Abhinav Kumar, Ronen E. Mukamel

Publication date: 4 April 2017

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.01924

zbMATH Keywords

correspondencesgenus-2 curves

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Jacobians, Prym varieties (14H40) Modular and Shimura varieties (14G35)

Related Items (8)

Billiards and Teichmüller curves ⋮ Hilbert modular surfaces for square discriminants and elliptic subfields of genus 2 function fields ⋮ Computing the geometric endomorphism ring of a genus-2 Jacobian ⋮ \(\mathrm{GL}_2\mathbb{R}\)-invariant measures in marked strata: generic marked points, Earle-Kra for strata and illumination ⋮ Rigorous computation of the endomorphism ring of a Jacobian ⋮ Billiards, quadrilaterals and moduli spaces ⋮ Existence of closed geodesics through a regular point on translation surfaces ⋮ Marked points on translation surfaces

Uses Software

• Magma

Cites Work

• Unnamed Item
• Splitting mixed Hodge structures over affine invariant manifolds
• K3 surfaces and equations for Hilbert modular surfaces
• Poncelet 5-gons and abelian surfaces
• General form of Humbert's modular equation for curves with real multiplication of \(\Delta =5\)
• Translation surfaces and their orbit closures: an introduction for a broad audience
• Dynamics of \(\text{SL}_2(\mathbb R)\) over moduli space in genus two
• Computing with the analytic Jacobian of a genus 2 curve
• Proving that a genus 2 curve has complex multiplication
• Billiards and Teichmüller curves on Hilbert modular surfaces
• Poonen's question concerning isogenies between Smart's genus 2 curves

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