Let $V=V(x_3-x_1^2,x_4-x_1x_3,x_2x_3-x_1x_5,x_4^2-x_3x_5)\subseteq \mathbb{C}^5$ be an affine variety. Is V a finite set of points?
I tried using Groebner bases, but I can not get anywhere. Could someone please help me?
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Do you understand the definition of $V$? – Erick Wong Jun 23 '15 at 03:13
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yes I understand, but only the definition of V is enough? – Cgomes Jun 23 '15 at 03:16
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If you can't tell from the plain definition of $V$ whether or not it's finite, it's hard to tell whether you do understand the definition :). This is a very simple set of equations. – Erick Wong Jun 23 '15 at 03:22
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I know, I just would like to confirm the answer. Thanks! – Cgomes Jun 23 '15 at 03:29
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Your question does not indicate this desire. It reads as if you have no idea where to begin. Please clarify your question. – Erick Wong Jun 23 '15 at 04:02
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I was wrong at the beginning.Thanks! – Cgomes Jun 23 '15 at 04:03
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I thought it was more difficult. Excuse me by mistake. I was study Grobner Basis and this problem was on the list. – Cgomes Jun 23 '15 at 04:06
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I think something in my answer here colud be usefull to you http://math.stackexchange.com/questions/595268/prime-maximal-ideals-of-mathbbcx-y-containing-a-given-ideal/595503#595503 – Sabino Di Trani Jun 23 '15 at 12:55
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HINT
You are living in $\mathbb C^5$.
You have four equations.
Then what is the minimal dimension your variety can have?
Fredrik Meyer
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