4 papers
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…
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…
Further results on Artin approximation, for group-actions on mapping-germs Maps(X,Y) and for quivers of maps
Dmitry Kerner
Consider (analytic, resp. algebraic) map-germs, Maps((k^n,o),(k^m,o)). These germs are traditionally studied up to the right, let-right and contact equivalences. Below G is one of…
Results on left-right approximation for algebraic morphisms and for analytic morphisms of weakly finite singularity type
Dmitry Kerner
The classical Artin approximation (AP) reads: any formal solution of a system of (analytic, resp. algebraic) equations of implicit function type is approximated by ``ordinary" solu…