# Finite Variety in $\mathbb{C}^5$

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?

• Do you understand the definition of $V$? – Erick Wong Jun 23 '15 at 3:13
• yes I understand, but only the definition of V is enough? – Cgomes Jun 23 '15 at 3:16
• 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 3:22
• I know, I just would like to confirm the answer. Thanks! – Cgomes Jun 23 '15 at 3:29
• 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 4:02

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