# Infinitely many exceptional divisors

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

• 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? – Tabes Bridges Dec 6 at 19:01