an:05963922
Zbl 1255.30046
Imayoshi, Yoichi; Ito, Manabu; Yamamoto, Hiroshi
On the number of holomorphic mappings between Riemann surfaces of finite analytic type
EN
Proc. Edinb. Math. Soc., II. Ser. 54, No. 3, 711-730 (2011).
00287137
2011
j
30F99
Riemann surface of finite analytic type; holomorphic mapping; Euler-Poincar?? characteristic
A Riemann surface is said to be of finite analytic type if it is a compact Riemann surface from which a finite set of points is removed. In the paper under review the authors consider the set of non-constant holomorphic mappings between two Riemann surfaces of finite analytic type, and give upper bounds on the cardinality of the set when the Euler-Poincar?? characteristic of the target surface is negative. The bounds are described by genera and the numbers of punctures of source and target surfaces. Furthermore the authors treat surfaces whose Euler-Poincar?? characteristic is non-negative.
Gou Nakamura (Toyota)