A rigid Calabi--Yau 3-fold

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 $Pic(\mathcal{Z})$....

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Bibliographic Details
Main Authors Filippini, Sara Angela, Garbagnati, Alice
Format Journal Article
LanguageEnglish
Published 09.02.2011
Subjects
Mathematics - Algebraic Geometry
Physics - High Energy Physics - Theory
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Summary: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.
DOI:10.48550/arxiv.1102.1854