A rigid Calabi--Yau 3-fold

Details A rigid Calabi--Yau 3-fold A rigid Calabi--Yau 3-fold

2011-02-09

arxiv.org/abs/1102.1854v2

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, Version 2: minor changes, references added

Scientific paper

The aim of this paper is to analyze some geometric properties of the rigid Calabi--Yau threefold $\mathcal{Z}$ obtained by a quotient of $E^3$, where $E$ is a specific elliptic curve. We describe the cohomology of $\mathcal{Z}$ and give a simple formula for the trilinear form on $Pic(\mathcal{Z})$. We describe some projective models of $\mathcal{Z}$ and relate these to its generalized mirror. A smoothing of a singular model is a Calabi--Yau threefold with small Hodge numbers which was not known before.

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