Does there exist a smooth, complex, projective 3-fold, with infinitely many divisors isomorphic to $\mathbb{CP}^{2}$ which have normal bundle $\mathcal{O}(-1)$?

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    $\begingroup$ Exercise 1.8 in my advisor's notes homepages.math.uic.edu/~coskun/utah-notes.pdf explains how to construct a surface with infinitely many $K_X$-negative extremal rays, although I'm not sure off the top of my head if these are actually $(-1)$-curves. Perhaps you could use a similar elliptic threefold construction? $\endgroup$ – Tabes Bridges Dec 6 '18 at 19:01

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