Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent

Guillaume Rond

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arXiv · 2503.08957

Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent

Guillaume Rond

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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 $\mathbb C^n$. More precisely we give an example of two germs of real algebraic surfaces in $\mathbb C^2$ that are biholomorphic, but not by means of an algebraic biholomorphism.

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Guillaume Rond. 2025-03-11. Real algebraic surfaces biholomorphically equivalent but not algebraically equivalent. https://arxiv.org/abs/2503.08957

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