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?

  • $\begingroup$ Do you understand the definition of $V$? $\endgroup$ – Erick Wong Jun 23 '15 at 3:13
  • $\begingroup$ yes I understand, but only the definition of V is enough? $\endgroup$ – Cgomes Jun 23 '15 at 3:16
  • $\begingroup$ 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. $\endgroup$ – Erick Wong Jun 23 '15 at 3:22
  • $\begingroup$ I know, I just would like to confirm the answer. Thanks! $\endgroup$ – Cgomes Jun 23 '15 at 3:29
  • $\begingroup$ Your question does not indicate this desire. It reads as if you have no idea where to begin. Please clarify your question. $\endgroup$ – Erick Wong Jun 23 '15 at 4:02


You are living in $\mathbb C^5$.

You have four equations.

Then what is the minimal dimension your variety can have?


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