Action of the Automorphism Group on the Jacobian of Klein's Quartic Curve

Learn about complex algebraic geometry and group theory through this 42-minute mathematics lecture that explores the quotient variety of the 3-dimensional Jacobian of Klein's quartic curve. Discover how the full automorphism group of order 336 relates to the 3-dimensional weighted projective space with weights 1,2,4,7, as demonstrated through joint research with Dimitri Markouchevitch. Examine the Bernstein and Schwarzman conjecture regarding quotients of n-dimensional complex spaces by irreducible complex crystallographic groups generated by reflections. Follow the detailed proof and understand the crucial role of computing the Hilbert function of the algebra of invariant theta-functions on the Jacobian in establishing this mathematical relationship.