Communications in Number Theory and Physics

Volume 10 (2016)

Number 3

A rigid Calabi–Yau manifold with Picard number two

Pages: 571 – 585



Eberhard Freitag (Mathematisches Institut, Heidelberg, Germany)


We study a projective Calabi–Yau threefold $\mathcal{Y}^{+}$ which has been constructed in [FS] (E. Freitag and R. Salvati-Manni, On Siegel threefolds with a projective Calabi–Yau model, Commun. Number Theory Phys. 5 2011, no. 3, 713–750.) It is rigid $(h^{12} = 0)$ and has Picard number $(h^{11} = 2)$. We construct a pair of divisors $\mathcal{D}^{\pm}$ which give a basis of $\mathrm{Pic}(\mathcal{Y}^{+}) \otimes_{\mathbb{Z}} \mathbb{Q}$ and determine all intersection numbers $\mathcal{D}^{\pm} \cdot \mathcal{D}^{\pm} \cdot \mathcal{D}^{\pm}$.

Published 15 November 2016