Q:

Triple of powers is subvariety?

Consider the set $B=\{(t^2,t^3,t^4)\mid t\in \mathbb{C}\}$. Is it a subvariety of $\mathbb{C}^3$? That is, is it the set of common zeros of some (finite number of) polynomials?
I'm thinking about $y^2-x^3$ and $z-x^2$. But suppose $x=t^2$, then we're allowing $y=\pm t^3$. How to get rid of $-t^3$?

A:

That $x = t^2$ allows $y = \pm t^3$ is no problem, because $(t^2, -t^3, t^4)$ is also in $B$ (just replace $t$ by $-t$).

