Classification of free actions on complete intersections of four quadrics

In this paper we classify all free actions of finite groups on Calabi–Yau complete intersection of four quadrics in $\mathbb{P}^7$, up to projective equivalence. We get some examples of smooth Calabi–Yau three-folds with large nonabelian fundamental groups. We also observe the relation between some of these examples and moduli of polarized abelian surfaces.

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Published 21 May 2012