Does $SL_n(\mathbb{R})$ (or $SL_n(\mathbb{C})$ ) have significance as an algebraic set?

Question

The determinant of a matrix is a polynomial in its entries, and the matrices in $SL_n(\mathbb{F})$, when written out as points in $\mathbb{F}^{n^2}$, are precisely the zero set of (said polynomial $-1$), which is an algebraic subset of $\mathbb{F}^{n^2}$.

Is there any meaningful algebro - geometric consequence of this?