Uniqueness Theorems for Parametrized Algebraic Curves
Copyright policy )Uniqueness Theorems for Parametrized Algebraic Curves
Let L 1 , … , L n {L_1}, \ldots ,{L_n} be lines in P 2 {\mathbb {P}^2} and let f , g : P 1 → P 2 f,g:{\mathbb {P}^1} \to {\mathbb {P}^2} be nonconstant algebraic maps. For certain configurations of lines L 1 , … , L n {L_1}, \ldots ,{L_n} , the hypothesis that, for i = 1 , … , n i = 1, \ldots ,n , the inverse images f − 1 ( L i ) {f^{ - 1}}({L_i}) and g − 1 ( L i ) {g^{ - 1}}({L_i}) are equal, not necessarily with the same multiplicities, implies that f f is identically equal to g g .
- Alabama Agricultural and Mechanical University United States
Special algebraic curves and curves of low genus, Projective techniques in algebraic geometry, Rational and birational maps, Value distribution theory in higher dimensions, algebraic maps, inverse images of configurations of lines
Special algebraic curves and curves of low genus, Projective techniques in algebraic geometry, Rational and birational maps, Value distribution theory in higher dimensions, algebraic maps, inverse images of configurations of lines
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