2007/03/27 by Kapustka, Grzegorz, Grzegorz Kapustka, Kapustka, Michal · 1 citation
Mathematics · #14J10 #14J32 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.math/0703810
openalex publication_date 2007/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct examples of primitive contractions of Calabi--Yau threefolds with exceptional locus being ℙ1 × ℙ1, ℙ2, 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 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.