Brian Jurgelewicz

Klein's Quartic and (2,3,7)

Klein's quartic is the plane curve given by the equation x^3y+y^3z+z^3x = 0. It's automorphism group, PSL_2(Z/7Z), has order 168, the maximum possible for a curve of genus 3. The surface singularity x^2+y^3+z^7 = 0 appears as a quotient of the cone over Klein's curve. This talk will be a gentle introduction to these two interesting objects.