Séance Séminaire

Séminaire Gaston Darboux

Drawing the complex projective structures on once-punctured tori.

Associated with the complex projective structure on Riemann surface X, we can consider the developing map and the holonomy representation of the fundamental group of X. Let K(X) be the set of complex projective structures on X whose holonomy groups are discrete. When X is a once-punctured torus, we can produce pictures of K(X) in the complex plane, which reflect the rich geometric structure of K(X). This is a joint work with Toshiyuki Sugawa (Hiroshima), Masaaki Wada (Nara) and Yasushi Yamashita (Nara).