Threefolds whose canonical bundles are not numerically effective.
Let X be an arbitrary nonsingular projective 3-fold whose canonical bundle is not numerically effective. Then we have: (i) X contains an exceptional divisor of several types, which we classify explicitly, (ii) X has a morphism to a projective nonsingular surface whose fibers are conics, (iii) X has a morphism to a projective nonsingular curve whose general fibers are Del Pezzo surfaces, or (iv) X is a Fano 3-fold with Picard number 1.
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Mathematics Department, Harvard University, Cambridge, Massachusetts 02138.