Let $V_1,V_2$ be affine varieties. Let $f$ be a morphism(https://en.wikipedia.org/wiki/Morphism_of_algebraic_varieties) between $V_1,V_2$.
If $f$ is bijective, is inver of $f$ also morphism ? If not, I would be appreciated if you could've me some examples.
Thank you for your help.
No. The simplest example is the morphism $$ \mathrm{Spec}(\Bbbk[t]) \to \mathrm{Spec}(\Bbbk[x,y]/(y^2 - x^3)), \qquad x = t^2,\ y = t^3. $$