Exotic affine space

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

$\{(z_1,z_2,z_3,z_4)\in {ℂ}^4|z_1+z_1^2{z}_2+z_3^3+z_4^2=0\}.$

References

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