I'm currently preparing for exam and I'm stuck on a question from some old exam:
Data: $Y=\mathbb{P}_{\bar{w} }^{1}\times \mathbb{P}_{\bar{u}}^{1} $
$A=\left \{ (\bar{w},\bar{u}) \in Y:w_{0}^{2}u_{1}+w_{1}^{2}u_{0}=0 \right \} $
$B=\left \{ (\bar{w},\bar{u}) \in Y:w_{0}u_{1}^{2}+w_{1}u_{0}^{2}=0 \right \} $
Let us denote by $\bar{A}$ and $\bar{B}$ the simple divisors defined by $A$ and $B$.
Prove that $\bar{A} \nsim \bar{B}$.
Find the $(\bar{A},\bar{B})$, intersection number of $A$ and $B$
Is the intersection of $A$ and $B$ on point $a=((1,-1),(1,-1))$ it transversal?
Thanks a lot!