Primitive contractions of Calabi-Yau threefolds I

Details Primitive contractions of Calabi-Yau threefolds I Primitive contractions of Calabi-Yau threefolds I

2007-03-27

arxiv.org/abs/math/0703810v3

Mathematics

Algebraic Geometry

23 pages, the numeration of subarticles changed

Scientific paper

We construct examples of primitive contractions of Calabi--Yau threefolds with exceptional locus being $ \mathbb{P}^1 \times \mathbb{P}^1$, $\mathbb{P}^2$, and smooth del Pezzo surfaces of degrees $\leq 5$. 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 a generic fiber of the smoothing family of each 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.

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