Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent
Complex Variables
2026-05-27 v4 Algebraic Geometry
Combinatorics
Abstract
We answer in the negative the long-standing open question of whether biholomorphic equivalence implies algebraic equivalence for germs of real algebraic manifolds in . More precisely we give an example of two germs of real algebraic surfaces in that are biholomorphic, but not by means of an algebraic biholomorphism.
Cite
@article{arxiv.2503.08957,
title = {Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent},
author = {Guillaume Rond},
journal= {arXiv preprint arXiv:2503.08957},
year = {2026}
}