Exotic affine space explained

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} .^{[1] [2] [3]} 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 |z} ^{1+ z} ^{2 z} ^{2+ z} ^{2=0 \}.} ^{4}

Notes and References

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3. On exotic algebraic structures on affine spaces . alg-geom/9506005 . 2000 . Mikhail . Zaidenberg . 1995alg.geom..6005Z . St. Petersburg Mathematical Journal . 11 . 5 . 703–760.