Algebraic approximation of analytic sets and mappings

Details Algebraic approximation of analytic sets and mappings Algebraic approximation of analytic sets and mappings

2007-12-19

arxiv.org/abs/0712.3261v1

J. Math. Pures Appl. 90 (2008) 312-327

Mathematics

Complex Variables

23 pages

Scientific paper

Let {X_n} be a sequence of analytic sets converging to some analytic set X in the sense of holomorphic chains. We introduce a condition which implies that every irreducible component of X is the limit of a sequence of irreducible components of the sets from {X_n}. Next we apply the condition to approximate a holomorphic solution y=f(x) of a system Q(x,y)=0 of Nash equations by Nash solutions. Presented methods allow to construct an algorithm of approximation of the holomorphic solutions.

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