Q: Principal divisor on a projective curve has degree zero In the book "Algebraic Geometry" of Hartshorne, in corollary 6.10 chapter 2, he wants to prove that principal divisors have degree zero. To do this he takes $f\in K(X)^*$ and this gives a morphism $\phi: X\rightarrow \mathbb{P}^1$. Now he says that $(f)=\phi^*(0-\infty)$, why is this true?
