Calabi-Yau construction by smoothing normal crossing varieties

TL;DR

This paper explores a novel method for constructing Calabi-Yau manifolds by smoothing normal crossing varieties, providing theoretical tools for Picard group calculations and producing new examples with specific properties.

Contribution

It introduces a new construction technique for Calabi-Yau manifolds via smoothing, along with methods to compute their Picard groups and examples with Picard number one.

Findings

Developed theories for Picard group calculations of smoothed Calabi-Yau manifolds

Constructed new Calabi-Yau 3-folds with Picard number one

Provided applications demonstrating the method's effectiveness

Abstract

We investigate a method of construction of Calabi--Yau manifolds, that is, by smoothing normal crossing varieties. We develop some theories for calculating the Picard groups of the Calabi--Yau manifolds obtained in this method. Some applications are included, such as construction of new examples of Calabi--Yau 3-folds with Picard number one with some interesting properties.