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Reference for Algebraic Geometry

I'm rather clueless about this exercise. What is a Zariski closure? What topics/books should I read on to gain some knowledge on solving akin exercises? (I don't want help in solving the exercise)

Exercise:

Let $Z$ be the Zariski closure in $A^4$ of the set $\lbrace (n, 2^n, 3^n, 6^n)\rbrace$, for $n \in \mathbb{N}$.

What dimension does $Z$ have on $\mathbb{C}$? Find generators for its ideal in $\mathbb{C}[X_1, X_2, X_3, X_4]$.

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nareto
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    You already received a partial answer on MathOverflow. Please do not hide that fact. http://mathoverflow.net/questions/71302/what-is-a-zariski-closure-closed – Tsuyoshi Ito Jul 26 '11 at 13:02
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    You want to learn some algebraic geometry. Look at this thread and this thread and this thread and this thread, for example. – t.b. Jul 26 '11 at 13:02
  • I voted to close this question as a duplicate, as it is asking for references only, and these are covered in the threads I mentioned in my previous comment. – t.b. Jul 26 '11 at 13:20
  • thanks Theo. Why didn't you make your comment an answer? I probably would have chosen it. – nareto Jul 26 '11 at 13:40
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    I'm invoking mod super power to close this as duplicate as the OP is already aware of the terminology "algebraic geometry" from his original choice of tags for the question, so this is not the case of someone not knowing that the concept of "Zariski closure" can be learned from a textbook on algebraic geometry. – Willie Wong Jul 26 '11 at 14:05
  • well I had heard that the Zariski topology was an algebraic geometry topic, so I suspected the Zariski closure had something to do with it, that's why I thought of tagging it. Of course this is not allways the case, so I was not sure I would find what I needed on an algebraic geometry text (i.e. there are topics with similar names but with totally different content, for example Gauss' Lemma) – nareto Jul 26 '11 at 14:46

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