UTM Ideals Varieties and Algorithm - Chapter 1 Section 2 Exercise 5

Problem:

Solution:

This is the variety $\mathbf{V}(x - 2, y, z + 1) \cup \mathbf{V}(x^2 - y)$. Therefore ,the answer is the single point $(2, 0, -1)$ together with a parabola $y = x^2$ extended to become a surface with arbitrary value $z$. The point is not on the surface itself so it stands out as a singular point.