Exotic affine space

In algebraic geometry, an exotic affine space is a complex algebraic variety that is diffeomorphic to ${\displaystyle \mathbb {R} ^{2n}}$ for some n, but is not isomorphic as an algebraic variety to ${\displaystyle \mathbb {C} ^{n}}$.^[1][2][3] An example of an exotic ${\displaystyle \mathbb {C} ^{3}}$ is the Koras–Russell cubic threefold,^[4] which is the subset of ${\displaystyle \mathbb {C} ^{4}}$ defined by the polynomial equation

${\displaystyle \{(z_{1},z_{2},z_{3},z_{4})\in \mathbb {C} ^{4}|z_{1}+z_{1}^{2}z_{2}+z_{3}^{3}+z_{4}^{2}=0\}.}$