Let $\mathfrak{g}$ be an algebraic Lie algebra and $V$ be a $\mathfrak{g}$-module, then for each $v\in V$, define $\mathfrak{g}^v = \{x\in\mathfrak{g}:xv = 0\}$. Let $V_{reg}$ be the set of all $v$ such that $\mathfrak{g}^v$ has minimal dimension.
I was reading a paragraph and it claims that $V_{reg}$ is open dense in $V$ (in the Zariski topology). So I need to show that the complement of $V_{reg}$ is an algebraic set, but I'm not sure how to see this, please help.