The Klein Quartic
نویسنده
چکیده
Figure 1: Fundamental region R of the Modular Group, given by {z ∈ H : |z| > 1,− 2 ≤ Re(z) ≤ 1 2} The Klein Quartic curve is famous for its symmetries and many visualizations are created to capture these in lower dimensions. In fact, it has the largest possible automorphism group for its genus, the simple group of order 168. Yet, interest in this algebraic curve started with knowledge of the existence of this large group, and the work that had to be done to express its action on an algebraic curve is often overlooked. Thus, this paper aims to give a historical account of the steps that led to the discovery of the equation of the Klein Quartic surface in projective coordinates.
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