A rigid Calabi--Yau 3-fold
Abstract
The aim of this paper is to analyze some geometric properties of the rigid Calabi--Yau threefold Z obtained by a quotient of E3, where E is a specific elliptic curve. We describe the cohomology of Z and give a simple formula for the trilinear form on Pic(Z). We describe some projective models of 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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