Homeomorphism versus isomorphism for varieties (Q1262911)

Let f: \(Y\to X\) be a morphism of algebraic varieties over a fixed algebraically closed field, which is birational and a homeomorphism of the underlying topological spaces. If X is weakly normal [\textit{A. Andreotti} and \textit{E. Bombieri}, Ann. Sc. Norm. Super. Pisa, Sci. Fis. Mat., III. Ser. 23, 431-450 (1969; Zbl 0184.245)]), it was assumed by several authors (the papers are indicated) that then f is an isomorphism of varieties. In the paper, the author gives a counterexample to this assumption and proves that it is true under the assumption that X has no one-dimensional components. - As a corollary he obtains a characterization of the weak normalization of a variety X without one-dimensional components.