Calabi-Yau Threefolds With Small Hodge Numbers

TL;DR

This paper compiles an updated list of Calabi-Yau threefolds with small Hodge numbers, emphasizing those with holonomy exactly SU(3), based on recent computations and constructions.

Contribution

It provides the first comprehensive list of such Calabi-Yau threefolds with small Hodge numbers, incorporating new data from recent calculations and constructions.

Findings

Most Hodge numbers computed from free quotients of complete intersections.

Updated Hodge plot with new points added.

Enhanced understanding of Calabi-Yau threefolds with small height.

Abstract

We present a list of Calabi-Yau threefolds known to us, and with holonomy groups that are precisely SU(3), rather than a subgroup, 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 free quotients of complete intersection Calabi-Yau threefolds, most of which were computed in Refs. [1-3] and the remainder in Ref. [4], many new points have been added to the tip of the Hodge plot, updating the reviews by Davies and Candelas in Refs. [1, 5]. In view of this and other recent constructions of Calabi-Yau threefolds with small height, we have produced an updated list.