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

TL;DR

This paper explores hyperquotient singularities called hyperconifolds in the moduli space of Calabi-Yau threefolds, showing they can lead to new topological transitions and the construction of novel Calabi-Yau manifolds.

Contribution

It introduces hyperconifolds as a new class of singularities in Calabi-Yau threefolds and demonstrates their potential to generate new compact Calabi-Yau manifolds through topological transitions.

Findings

Hyperconifolds are described as hyperquotient singularities of the conifold.

Many hyperconifold singularities can be resolved to produce new Calabi-Yau manifolds.

The study provides a method for embedding and resolving these singularities in compact Calabi-Yau varieties.

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 realised in string theory.