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Exercise 111.61.7. Let $k$ be an algebraically closed field. Let $S \subset \mathbf{P}^3_ k$ be a smooth hypersurface of degree $d$. Assume that $S$ contains a line $\ell $. What is the self square of $\ell $ viewed as a divisor on $S$?

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View Exercise 111.61.7 as pdf