Quotients of the conifold in compact Calabi-Yau threefolds, and new topological transitions

Abstract

The moduli space of multiply connected Calabi–Yau threefolds is shown to contain codimension-one loci on which the corresponding variety develops a certain type of hyperquotient singularity. These have local descriptions as discrete quotients of the conifold, and are referred to here as hyperconifolds. In many (or possibly all) cases such a singularity can be resolved to yield a distinct compact Calabi–Yau manifold. These considerations therefore provide a method for embedding an interesting class of singularities in compact Calabi–Yau varieties, and for constructing new Calabi–Yau manifolds. It is unclear whether the transitions described can be realized in the string theory.