Trisha Shetty (Editor)

Exotic affine space

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In algebraic geometry, an exotic affine space is a complex algebraic variety that is diffeomorphic to R 2 n 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 ) C 4 | z 1 + z 1 2 z 2 + z 3 3 + z 4 2 = 0 } .

References

Exotic affine space Wikipedia