On homeomorphisms preserving principal divisors
Author: Yosef Stein
Journal: Proc. Amer. Math. Soc. 83 (1981), 557-562
MSC: Primary 14H15; Secondary 30F20
MathSciNet review: 627691
Abstract: Let and be compact Riemann surfaces of genus . Let be a continuous map. The map induces a group homomorphism from the group of divisors on into the group of divisors on . This group homomorphism will be denoted by the same letter throughout this paper. If is a divisor on , then . If is a holomorphic or an anti-holomorphic homeomorphism, then is a principal divisor on if is a principal divisor on . To what extent is the converse of this statement true?
The answer to this question is provided by Theorem 1 of this paper: If is a principal divisor on whenever is a principal divisor on , then is either a holomorphic or an anti-holomorphic homeomorphism.
-  R. C. Gunning, Lectures on Riemann surfaces, Princeton Mathematical Notes, Princeton University Press, Princeton, N.J., 1966. MR 0207977
-  R. C. Gunning, Lectures on Riemann surfaces, Jacobi varieties, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Mathematical Notes, No. 12. MR 0357407