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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Uniqueness theorems for parametrized algebraic curves

Author: Peter Hall
Journal: Trans. Amer. Math. Soc. 341 (1994), 829-840
MSC: Primary 32H25; Secondary 14E05, 32H04
MathSciNet review: 1144014
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Abstract: Let $ {L_1}, \ldots ,{L_n}$ be lines in $ {\mathbb{P}^2}$ and let $ f,g:{\mathbb{P}^1} \to {\mathbb{P}^2}$ be nonconstant algebraic maps. For certain configurations of lines $ {L_1}, \ldots ,{L_n}$, the hypothesis that, for $ i = 1, \ldots ,n$, the inverse images $ {f^{ - 1}}({L_i})$ and $ {g^{ - 1}}({L_i})$ are equal, not necessarily with the same multiplicities, implies that $ f$ is identically equal to $ g$.

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Article copyright: © Copyright 1994 American Mathematical Society