Type III contractions and quintic threefolds

2020/10/26 by Grzelakowski, Kacper
#14J30 #14J32 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.13866

Abstract

We study type III contractions of Calabi-Yau threefolds containing a ruled surface over a smooth curve. We discuss the conditions necessary for the image threefold to by smoothable. We describe the change in Hodge numbers caused by this contraction and smoothing deformation. A generalization of a fomula for calculating Hodge numbers of hypersurfaces in ℙ⁴ with ordinary double and triple points is presented. We use these results to construct new Calabi-Yau threefolds of Picard rank two arising from a family of quintic threefolds containing a cone.

Related

• Primitive contractions of Calabi-Yau threefolds I
• Projections of del Pezzo surfaces and Calabi--Yau threefolds
• Geometry and arithmetic of non-rigid families of Calabi-Yau 3-folds; questions and examples
• Clemens' conjecture: part I
• Geometry and arithmetic on a quintic threefold