I'm trying to figure out if various polynomial maps are finite, on map I'm considering is $\mathbb{A}^1 \rightarrow V(y^2 - x^3) $ that maps $t$ to $(t^2, t^3)$.
So I'm thinking that because this is a bijection, then it is finite. But to be honest I'm not sure if this is the case as I'm not entirely sure what makes a polynomial a finite map.