This paper relates two properties of varieties or rather of constructible sets. The first is the manner in which we can parametrize our sets, and we will be interested in polynomial parametrizations. The second is the fact that the set is etale exotic (see [4], [5], [6]). In the second section we will prove a theorem on polynomial parametrizations of complex spheres (Theorem 1). An n-dimensional complex sphere is the hypersurface in C~(n+1) which is defined by the equation X_1~2 + ··· + X_(n+1)~2 = 1 We will see that the complex sphere has a polynomial parametrization whenever it is even dimensional. We do not know the answer in the odd dimensional case. In the one dimensional case the answer is negative as can be seen easily.
展开▼
