Exotic affine space
In algebraic geometry, an exotic affine space is a complex algebraic variety that is diffeomorphic to R 2 n {\displaystyle \mathbb {R} ^{2n}} for some n, but is not isomorphic as an algebraic variety to C n {\displaystyle \mathbb {C} ^{n}} . An example of an exotic C 3 {\displaystyle \mathbb {C} ^{3}} is the Koras–Russell cubic threefold, which is the subset of C 4 {\displaystyle \mathbb {C} ^{4}} defined by the polynomial equation { ( z 1 , z 2 , z 3 , z 4 ) ∈ C 4 | z 1 + z 1 2 z 2 + z 3 3 + z 4 2 = 0 } .