Exotic affine space

In algebraic geometry, an exotic affine space is a complex algebraic variety that is diffeomorphic to $$\mathbb{R}^{2n}$$ for some n, but is not isomorphic as an algebraic variety to $$\mathbb{C}^n$$. An example of an exotic $$\mathbb C^3$$ is the Koras–Russell cubic threefold, which is the subset of $$\mathbb C^4$$ defined by the polynomial equation
 * $$\{(z_1,z_2,z_3,z_4)\in\mathbb C^4|z_1+z_1^2z_2+z_3^3+z_4^2=0\}.$$