This is from the following video - https://www.youtube.com/watch?v=fDdzg83z6Xc
The function is $f = \frac {y}{z}$
The curve is ${y^2}z - x^3 - x{z^2}$
The poles are $(0:0:1)$, $(1:0:i)$, $(1:0:-i)$
The zeros is $(0:1:0)$
I understood up to this.
But then, he writes down the divisor of $f$ on the curve as
$Div(f) = 1.(0:0:1) + 1.(1:0:i) + 1.(1:0:-i) - 1.(0:1:0)$
i.e. he is considering the co-efficient of the Pole as $1$. And the degree of the Divisor as $2$ & he says hence it's not a principal divisor.
As per Bezout's, won't the no of poles be equal to the number of zeros? Hence the co-efficient of the pole would be zero.
Can someone explain why the co-efficient of the pole is not 3?
And here is a link of the video timestamped to 7:36 where he describes this - https://youtu.be/fDdzg83z6Xc?t=456
Here is a screenshot of where he says this
