#todo > [!NOTE] Definition (Algebraic plane curve) > An *algebraic* [[Parametrized Curve|curve]] over a [[Field (Algebra)|field]] $K$ is the [[Preimage (of set under a function)|preimage]] of $\{ 0 \}$ under $f(x,y)$ where $f(x,y)$ is a [[Polynomial|polynomial]] in $K[x,y]$. # Properties