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math.AG2025
Andreotti-Frankel-Hamm theorem for morphisms of algebraic varieties
Dmitry Kerner
The classical Andreotti-Frankel-Hamm theorem reads: a complex affine algebraic variety B, of dim_\C B=n, has homotopy type of dim_\R\le n. We prove the relative version for morphis…
math.AG2025
Equivalence of germs (of mappings and sets) over k vs that over K
Dmitry Kerner
Consider real-analytic mapping-germs, (R^n,o)-> (R^m,o). They can be equivalent (by coordinate changes) complex-analytically, but not real-analytically. However, if the transformat…