Geometry of the Wiman–Edge pencil, I: algebro-geometric aspects

Abstract

In 1981 William L. Edge discovered and studied a pencil C of highly symmetric genus 6 projective curves with remarkable properties. Edge’s work was based on an 1895 paper of Anders Wiman. Both papers were written in the satisfying style of 19th century algebraic geometry. In this paper and its sequel Geometry of the Wiman–Edge pencil, II: hyperbolic, conformal and modular aspects (in preparation), we consider C from a more modern, conceptual perspective, whereby explicit equations are reincarnated as geometric objects.