A rigid Calabi-Yau manifold with Picard number two

TL;DR

This paper investigates a specific rigid Calabi-Yau threefold with Picard number two, constructing a divisor basis and calculating all intersection numbers to deepen understanding of its geometric properties.

Contribution

It provides an explicit construction of a divisor basis and computes intersection numbers for a particular rigid Calabi-Yau threefold with Picard number two.

Findings

Constructed a basis of divisors for the Calabi-Yau threefold.

Determined all intersection numbers among the divisors.

Confirmed the rigidity and Picard number of the manifold.

Abstract

We study a projective Calabi-Yau threefold which has been constructed in an earlier paper. It is rigid and has Picard number two. We construct a pair of divisors which give a basis of the Picard group and determine all intersection numbers of three divisors.