= Complexified Minkowski spacetime
{title2=$M_{\mathbb C}\cong\mathbb C^4$}
= Complexified Minkowski space
{synonym}
Allow the four affine Minkowski coordinates to take independent complex values, obtaining $M_{\mathbb C}\simeq\mathbb C^4$ with the holomorphic extension of the flat conformal metric. In two-spinor coordinates $x^{AA'}$, the metric is proportional to $\epsilon_{AB}\epsilon_{A'B'}dx^{AA'}dx^{BB'}$. The <twistor incidence relation> associates a <complex projective line> to each affine point; compactification adds the points at conformal infinity.
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