/sci/ - Science & Math

>>12594530
I can finish by using (2) of this Proposition from Fulton's book, since I also know that the pole of my [math]f[/math] has Riemann-Roch dimension greater than 1.
But my professor didn't present this and the proof is complicated, instead, he suggested to find a morphism [math]\varphi[/math] associated to this extension and show that its degree is 1 by using what we have and those basic relations between divisors, pullback and pushforward, like [math] \text{deg}(\varphi^* D) = (\text{deg }\varphi) (\text{deg } D)[/math]. I don't see a solution here... I thought of trying to define [math]\varphi[/math] by [math]Q\mapsto (x_1(Q) : x_2(Q))[/math] for suitable [math]x_1, x_2\in k[C][/math] with [math]x = x_1/x_2[/math], but I don't even know if this is well-defined.