Constructive Approximation

, Volume 35, Issue 3, pp 273-291

First online:

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Approximation of Analytic Sets with Proper Projection by Algebraic Sets

  • Marcin BilskiAffiliated withDepartment of Mathematics and Computer Science, Jagiellonian University Email author 


Let X be an analytic subset of U×C n of pure dimension k such that the projection of X onto U is a proper mapping, where UC k is a Runge domain. We show that X can be approximated by algebraic sets. Next we present a constructive method for local approximation of analytic sets by algebraic ones.


Analytic set Algebraic set Nash set Approximation Holomorphic chain Markov’s inequality Normalization

Mathematics Subject Classification (2010)

32C25 41A10 32E30 14Q99