At the projective algebraic curves there are similar identities to affine curves.
Intersection points of projective algebraic curves.
The meanings
- order of point of the curve $F$
- intersection multiplicity of algebraic
are defined similarily.
If $z \neq 0$ we correspond $P=[x, y, 1]$ to the affine $[x, y, 1]$ and we calculate at it the order and the intersection multiplicity.
If $z=0$ then we apply the appropriate dehomogenization so that the Line $z=0$ becomes finite (for example we set $y=0$ and we "send" $y$ to infinity).
Can you explain to me the case $z=0$ :
If $z=0$ then we apply the appropriate dehomogenization so that the Line $z=0$ becomes finite (for example we set $y=0$ and we "send" $y$ to infinity).