What is the best way to find an actual divisor of an affine curve? I.E. if I am interested in finding a canonical divisor of a curve in two variables, is there a general way to go about it? Do I need to consider a projection on the x-axis?
I should clarify. I'm assuming the field is characteristic 0, and the curve is affine of the form f(x,y)=0. I computed the closure in P2, it was smooth, and am now trying to compute a canonical divisor on this curve. Thanks for the comments am reading up on it now.