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Jan 24, 2013 at 8:25 comment added Sándor Kovács I see. That makes more sense. Perhaps you should edit the question...(say add the ring in which you are working).
Jan 24, 2013 at 3:30 comment added Brett Parker To clarify, I meant that every holomorphic function on U which vanishes on $V$ may be written as a sum of holomorphic functions times polynomials in $I_V$.
Jan 24, 2013 at 3:27 answer added Brett Parker timeline score: 2
Jan 24, 2013 at 3:13 comment added Sándor Kovács holomorphic functions will probably not be generated by polynomials. did you mean regular functions on $U$?
Jan 24, 2013 at 1:24 history asked Brett Parker CC BY-SA 3.0