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I have been dealing with a problem and I could not find any tools to attack it. The problem is the following,

What extra conditions do I need to show that an affine smooth complete intersection variety is connected?

thanks for the answer and sorry for the sloppiness

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the problem deals with varieties which have dimension higher than 24. – guest Jun 17 '13 at 16:42
What kind of conditions are you looking for? In the affine case, it is usually difficult to say something is connected. – Mohan Jun 17 '13 at 19:03
yes it is affine. – guest Jun 18 '13 at 8:57
I thought of homogenizing the vanishing ideal and use the exercise Chapter II 8.4 [Compelete Intersection] which involves Unimixedness Thm (but do I really need that my Ring is Cohen-Macaulay) . OR to do some Bertini type trick since i have an equidimensional variety. Cut with "good" hyperplanes and try to end up with a curve it works specific cases but i cant prove it for general cases. I really appreciate the comment. – guest Jun 18 '13 at 9:09

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