Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 065, 20 pages      arXiv:1206.6004      https://doi.org/10.3842/SIGMA.2012.065
Contribution to the Special Issue “Geometrical Methods in Mathematical Physics”

Bring's Curve: its Period Matrix and the Vector of Riemann Constants

Harry W. Braden and Timothy P. Northover
School of Mathematics, Edinburgh University, Edinburgh, Scotland, UK

Received June 10, 2012, in final form September 27, 2012; Published online October 02, 2012

Abstract
Bring's curve is the genus 4 Riemann surface with automorphism group of maximal size, S5. Riera and Rodríguez have provided the most detailed study of the curve thus far via a hyperbolic model. We will recover and extend their results via an algebraic model based on a sextic curve given by both Hulek and Craig and implicit in work of Ramanujan. In particular we recover their period matrix; further, the vector of Riemann constants will be identified.

Key words: Bring's curve; vector of Riemann constants.

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