I tried to solve this question but not sure that my solution was the right one. Help me please with this question:
Find $\dim X\times \mathbb{P}^{2}$, where $X=\left \{ w_{0}^{3}=w_1(w_{1}^{2}-w_{2}^{2}) \right \}\subseteq \mathbb{P}_{w}^{2}$
Thanks!