Rhys Davies

Hyperconifold singularities and transitions



Abstract

I will introduce hyperconifold singularities, which are point-like threefold singularities given by finite quotients of the conifold, and arise naturally in compact varieties which lie on the boundary of moduli spaces of smooth multiply-connected Calabi-Yau threefolds. These varieties admit projective crepant resolutions, giving rise to new topological transitions -- hyperconifold transitions -- between compact Calabi-Yau manifolds. They are related to ordinary conifold transitions by mirror symmetry, but can change the fundamental group as well as the Hodge numbers.