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- W4250035353 abstract "Let ${S_1}$ and ${S_2}$ be compact Riemann surfaces of genus $g > 1$. Let $tau :{S_1} to {S_2}$ be a continuous map. The map $tau$ induces a group homomorphism from the group of divisors on ${S_1}$ into the group of divisors on ${S_2}$. This group homomorphism will be denoted by the same letter $tau$ throughout this paper. If $D = sum _{i = 1}^n{m_i}{p_i}$ is a divisor on ${S_1}$, then $tau (D) = sum _{i = 1}^n{m_i}tau ({p_i})$. If $tau$ is a holomorphic or an anti-holomorphic homeomorphism, then $tau (D)$ is a principal divisor on ${S_2}$ if $D$ is a principal divisor on ${S_1}$. To what extent is the converse of this statement true? The answer to this question is provided by Theorem 1 of this paper: If $tau (D)$ is a principal divisor on ${S_2}$ whenever $D$ is a principal divisor on ${S_1}$, then $tau$ is either a holomorphic or an anti-holomorphic homeomorphism." @default.
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- W4250035353 date "1981-11-01" @default.
- W4250035353 modified "2023-09-27" @default.
- W4250035353 title "On Homeomorphisms Preserving Principal Divisors" @default.
- W4250035353 doi "https://doi.org/10.2307/2044118" @default.
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