I didn't understand this notation in the chapter 7 page 93 of Fulton's algebraic curves book:
What the author means by $\text{ord}_Q(g)$?
Maybe he would like to say $\text{ord}_Q(G) := \text{ord}_P(g)$?
I need help
Thanks in advance
2026-03-28 20:09:33.1774728573
Meaning of notation $\operatorname{ord}_Q(g)$ in "Algebraic Curves" by Fulton
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Fulton denotes $\mbox{ord}_{P}(C)$ to be the order function on $k(C)$ defined by $\mathcal{O}_{P}(C)$. Where $C$ is an arbitrary curve and $P$ is a point on that curve. This is found on the first two paragraphs of chapter 7, Resolution of Singularities, section 7.1, page 81.
Hopefully this can give you some insight on how this applies to $\mbox{ord}_{Q}(G)$.