Advances in Theoretical and Mathematical Physics

Volume 15 (2011)

Number 6

A rigid Calabi–Yau three-fold

Pages: 1745 – 1787



Sara Angela Filippini (Dipartimento di Scienze e Alta Tecnologia, Università dell’Insubria)

Alice Garbagnati (Dipartimento di Matematica, Università di Milano)


The aim of this paper is to analyze some geometricproperties of the rigid Calabi–Yau three-fold$\mathcal{Z}$ obtained by a quotient of $\EEE$, where $E$is a specific elliptic curve. We describe the cohomology of$\mathcal{Z}$ and give a simple formula for the trilinearform on $\mathrm{Pic}(\mathcal{Z})$. We describe someprojective models of $\mathcal{Z}$ and relate these to itsgeneralized mirror. A smoothing of a singular model is aCalabi–Yau three-fold with small Hodge numbers which wasnot known before.

Full Text (PDF format)