Dr Andrei Constantin

Abstract:

We complete the study of smooth $Z_3$-quotients of complete intersection Calabi-Yau threefolds by discussing the six new manifolds that admit free $Z_3$ actions that were discovered discovered recently by Braun. These manifolds were missed in an earlier work and complete the web of smooth $Z_3$-quotients in a nice way. We discuss the transitions between these manifolds and include also the other manifolds of the web. This leads to the conclusion that the web of $Z_3$-free quotients of complete intersection Calabi-Yau threefolds is connected by conifold transitions.

Abstract:

We present a master list of Calabi-Yau threefolds, known to us, with small Hodge numbers, which we understand to be those manifolds with height $(h^{1,1}+h^{2,1})\le 24$. With the completion of a project to compute the Hodge numbers of all free quotients of complete intersection Calabi-Yau threefolds by Candelas et. al. in [1-3], many new points have been added to the tip of the Hodge plot, updating the reviews by Davies and Candelas in [1,4]. In view of this and other recent constructions of Calabi-Yau threefolds with small height we have produced an updated list.