That's actually trivially simple: if [f1,f2,f3] is the basis of your 
Riemann-Roch space, you just consider the map defined by [f1:f2:f3]. So you 
lift f1,f2,f3 to rational functions on the affine space that contains your 
curve: you just take the rational function representation and forget the 
algebraic relations between the variables. 


f1, f2, f3 are univariate polynomials (say in y) over rational function 
field (say in x). Then x and y are not always the variables X and Y of the 
coordinate ring of the affine plane. Things are more complicated if the 
curve is in space (of dim > 2).

 

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