François Bernard, Goulwen Fichou, Jean-Philippe Monnier, Ronan Quarez
Published 2022-03-18Version 1
We address the question under which conditions a bijective morphism between algebraic varieties over an algebraically closed field of characteristic zero is an isomorphism. Our two answers involve a study of seminormalization and saturation for morphisms between algebraic varieties, together with an interpretation in terms of continuous rational functions on the closed points of an algebraic variety. The continuity refers here to the usual Euclidean continuity in the complex case, and comes from the theory of real closed fields otherwise.
A notion of seminormalization for real algebraic varieties
The index of an algebraic variety
Cyclic coverings and higher order embeddings of algebraic varieties
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