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I am reading the following paper on the Cox ring of $\overline{M}_{0,6}$ by Ana-Maria Castravet:

I am stuck on an intersection-theoretic question, which appears as formula (9.1) in the above paper. It says the following:

Let $X=\mathbb{P}^3$ be the projective space and let $p_1,\ldots,p_5$ be 5 general points in $X$. Let $l_{ij}$ be the line passing through $p_i,p_j$. Let $Y$ be the blowup of $X$ along the points $p_i$ with exceptional divisors $E_i'$. Let $\pi:Z→Y$ be the blowup of $Y$ along the proper transforms of the lines $l_{ij}$. Let $E_i=\pi^{-1}(E_i')$.

We have $E_i$ is the blowup of $E_i'\cong \mathbb{P}^2$ at four points corresponding to the lines $l_{ij}$. Then why is it true that $E_i|_{E_i}=-H$, where $H$ is the hyperplane class on $E_i$?

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