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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 $B$.

  1. Prove that $\bar{A} \nsim \bar{B}$.

  2. Find the $(\bar{A},\bar{B})$, intersection number of $A$ and $B$

  3. Is the intersection of $A$ and $B$ on point $a=((1,-1),(1,-1))$ it transversal?

Thanks a lot!

  • 1
    Dear Lilly, you should suppress the bars on your letters: they are *all* confusing and useless.2012-08-14

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