Uniformizing Real Hyperelliptic M-Curves Using the Schottky–Klein Prime Function

DOI10.1007/978-3-642-17413-1_5zbMath1214.30033OpenAlexW2287325218MaRDI QIDQ5390266

Darren G. Crowdy, Jonathan S. Marshall

Publication date: 1 April 2011

Published in: Computational Approach to Riemann Surfaces (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-17413-1_5

zbMATH Keywords

Schottky-Klein prime functionexplicit conformal slit mappingreal hyperelliptic \(M\)-curvesSchottky uniformization of algebraic curves

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Real-analytic and semi-analytic sets (14P15) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

Uses Software

• SKPrime

Cites Work

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• Geodesics, periods, and equations of real hyperelliptic curves
• Computing the Schottky-Klein prime function on the Schottky double of planar domains
• Numerical Schottky uniformizations
• Schwarz–Christoffel mappings to unbounded multiply connected polygonal regions
• Introduction to Compact Riemann Surfaces
• Analytical formulae for the Kirchhoff–Routh path function in multiply connected domains
• The Schwarz–Christoffel mapping to bounded multiply connected polygonal domains
• Theta functions, kernel functions, and Abelian integrals

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