= Complexified compactified Minkowski space
{title2=$\mathbb M_{\mathbb C}=\operatorname{Gr}(2,\mathbb C^4)$}
The four-complex-dimensional <Grassmannian> of two-planes in <twistor space>. Its <Plücker embedding> is the <Klein quadric>. An affine chart consists of graphs $W_x=\{(ix\pi,\pi)\}$. A <Lorentzian reality structure on twistor space> or an <Euclidean reality structure on twistor space> selects different four-real-dimensional compact spacetimes inside this same complex manifold.
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