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math.AG2026
Invariants of real affine varieties based on their complexifications
Juliusz Banecki
We introduce a new family of invariants of real algebraic sets defined in terms of the topology of their complexifications and compute some of these invariants for spheres. This al…
math.AG2026
Optimal embedding dimension in the Nash--Tognoli theorem
Juliusz Banecki
We prove that every smooth compact submanifold of can be approximated up to a small isotopy by the real locus of a nonsingular complex algebraic subset of $\C^n$ defined ove…