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Primitive contractions of Calabi–Yau threefolds
"... Abstract. We construct examples of primitive contractions of Calabi–Yau threefolds with exceptional locus being P 1 × P 1, P 2, and smooth del Pezzo surfaces of degrees ≤ 5. We describe the images of these primitive contractions and find their smoothing families. In particular we give a method to co ..."
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Abstract. We construct examples of primitive contractions of Calabi–Yau threefolds with exceptional locus being P 1 × P 1, P 2, and smooth del Pezzo surfaces of degrees ≤ 5. We describe the images of these primitive contractions and find their smoothing families. In particular we give a method to compute the Hodge numbers of the generic fibers of the smoothings of each Qfactorial Calabi–Yau threefold with one isolated singularity obtained after a primitive contraction of type II. As an application we get examples of natural conifold transitions between some families of Calabi–Yau threefolds. 1.