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Does anyone know a recent survey in SCV? I am interested in famous problems such as The Union Problem, The Local Steiness Problem, The Intersection Problem, The Open Immersion Problem etc.

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    $\begingroup$ You should at the very minimum take the time to spell out SCV="several complex variables". $\endgroup$
    – Marc Palm
    Commented May 19, 2012 at 9:05
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    $\begingroup$ I totally agree, plus this should be cw, if it is to exist at all (I personally am of the opinion that if you have to ask you should not be in this business) $\endgroup$
    – Igor Rivin
    Commented May 19, 2012 at 12:38

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First google hit for "Open problems in SCV" yields

http://www.math.lsa.umich.edu/~fornaess/files/problems.pdf

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Corona Problem for more than one dimension on polydisk and unit ball is one that has resisted solution but partial results are available .

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