Genus 2 curves that admit a degree 5 map to an elliptic curve

DOI10.1515/FORUM.2009.027zbMath1174.14025arXiv1209.0443OpenAlexW2963706200MaRDI QIDQ3632762

Kay Magaard, Helmut Voelklein, Tanush Shaska

Publication date: 12 June 2009

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.0443

zbMATH Keywords

Hurwitz spacegenus 2 curvesgenus 1 curvesHumbert surface

Mathematics Subject Classification ID

Families, moduli of curves (algebraic) (14H10) Coverings of curves, fundamental group (14H30) Riemann surfaces; Weierstrass points; gap sequences (14H55)

Related Items (4)

Hilbert modular surfaces for square discriminants and elliptic subfields of genus 2 function fields ⋮ Isogenous components of Jacobian surfaces ⋮ Decomposing Jacobians Via Galois covers ⋮ Constructing Jacobian varieties with many elliptic curves

Uses Software

• GAP
• BRAID

Cites Work

• The inverse Galois problem and rational points on moduli spaces
• The moduli space of curves of genus two covering elliptic curves
• Diagonal quotient surfaces
• Modular diagonal quotient surfaces
• Covers of tori: genus two
• Arithmetic variety of moduli for genus two
• Curves of Genus 2 with Split Jacobian
• The number of curves of genus two with elliptic differentials.
• Humbert surfaces and the Kummer plane
• Large torsion subgroups of split Jacobians of curves of genus two or three
• Ein Satz über hyperellipitsche Funktionenkörper.

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