Singularities of Varieties

Tougerons Theorem
Theorem. If G is close to F, then G and F are analytically equivalent.
Proof. Given G close to F, we define an analytic isomorphism U :
(x, y) ↦→ (x + S(x,y), y + T(x,y)) such that F is close to F ◦ U and
ord(F ◦ U − G) > ord(F − G). Then we show that the composition of
these isomorphisms converges.
VO AAG 15