In algebraic geometry, an exotic affine space is a

complex algebraic variety In algebraic geometry, a complex algebraic variety is an algebraic variety (in the scheme sense or otherwise) over the field of complex number In mathematics, a complex number is an element of a number system that extends the real numbers ...

that is diffeomorphic to

\mathbb^

for some ''n'', but is not isomorphic as an algebraic variety to

\mathbb^n

. An example of an exotic

\mathbb C^3

is the

Koras–Russell cubic threefold In algebraic geometry, the Koras–Russell cubic threefolds are smooth affine complex threefolds diffeomorphic to \mathbf^3studied by . They have a hyperbolic action of a one-dimensional torus \mathbf^*with a unique fixed point, such that the qu ...

, which is the subset of

\mathbb C^4

defined by the polynomial equation :

\.

References

Algebraic varieties Diffeomorphisms {{geometry-stub