The <b>join</b> of two varieties $X,Y\subseteq \mathbb{P}^n$ is 
$$ J(X,Y) = \overline{\bigcup_{\substack{x\in X,~y\in Y\\x\ne y}} \ell(x,y)}$$
where $\ell(x,y)$ denotes the projective line through $x$ and $y$.