Nonisomorphic algebraic models of a smooth manifold
The paper contains the following result. Let M be a compact \(C^{\infty}\) manifold. Then there exists an uncountable family \(\{X_{\alpha}\}_{\alpha \in \Lambda}\) of nonsingular algebraic subsets of \({\mathbb{R}}^ n\), \(n=2\cdot \dim (M)+1,\) such that each \(X_{\alpha}\) is diffeomorphic to M, and \(X_{\alpha}\) is not birationally equivalent to \(X_{\beta}\) for \(\alpha\neq \beta\).
scientific article; zbMATH DE number 4175129