论文标题
III型收缩和三倍的五倍
Type III contractions and quintic threefolds
论文作者
论文摘要
我们研究了在平滑曲线上包含统治表面的Calabi-yau的III型收缩。我们讨论图像三倍到平滑的条件。我们描述了由于这种收缩和平滑变形引起的霍奇数量的变化。提出了用于计算$ \ mathbb {p}^4 $中的Hypersurfaces的Fomula的概括。我们使用这些结果来构建新的Calabi-yau三倍的Picard等级，由含有圆锥体的五重的三倍的家族产生。
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 $\mathbb{P}^4$ 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.
