Department of Mathematics

Instructor: D. Edidin

Description: This seminar based course will cover the theory curves and their moduli. We will begin with the classic material covered in Hartshorne Chapter III. Topics include, Riemann-Hurwitz formula, Riemann-Roch, linear systems and projective embeddings. We will then move on to discuss the construction of the moduli space of curves of a given genus. The problem construction of the moduli space occupied the attention of mathematicians beginning with Riemann and was ultimately settled by Mumford, Deligne and others. The study of moduli spaces of curves continues to be a very active and high-profile research area.