Algebraic characterizations of homeomorphisms between algebraic varieties [article]

François Bernard, Goulwen Fichou, Jean-Philippe Monnier, Ronan Quarez
2022 arXiv   pre-print
We address the question of finding algebraic properties that are respectively equivalent, for a morphism between algebraic varieties over an algebraically closed field of characteristic zero, to be an homeomorphism for the Zariski topology and for a strong topology that we introduce. Our 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
more » ... ic variety. The continuity refers to the strong topology which is the usual Euclidean topology in the complex case, whereas it comes from the theory of real closed fields otherwise.
arXiv:2203.09967v2 fatcat:l5qfw6ngsneethypb2ixhom4ja