A rigid Calabi-Yau manifold with Picard number two (Q505020)

This paper studies a projective Calabi-Yau threefold \(Y^{+}\) constructed in [\textit{E. Freitag} and \textit{R. Salvati Manni}, Commun. Number Theory Phys. 5, No. 3, 713--750 (2011; Zbl 1260.11036)]. \(Y^{+}\) is a rigid Calabi-Yau threefold and has Picard number \(h^{11}=2\). In this paper, a pair of divisors \(D^{\pm}\) is constructed. Such a pair gives a basis for the Picard group \(\text{{Pic}}(Y^+)\otimes_{\mathbb Z}\mathbb Q\). Also the intersection numbers \(D^{\pm}\cdot D^{\pm}\cdot D^{\pm}\) are computed.