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).