The join 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 $y$.
Jesko Hüttenhain
- 4.9k
- 32
- 73