Hodge Numbers for CICYs with Symmetries of Order Divisible by 4

TL;DR

This paper calculates the Hodge numbers of quotients of complete intersection Calabi-Yau three-folds by certain symmetry groups, expanding previous results to include cases with groups of order divisible by 4.

Contribution

It provides new computations of Hodge numbers for CICY quotients with symmetries of order divisible by 4, filling gaps in prior classifications.

Findings

Hodge numbers for quotients with Z_4 and Z_2 x Z_2 groups.

Hodge numbers for 99 CICYs with Z_2 quotients.

Extension of previous results on group actions with orders divisible by 4.

Abstract

We compute the Hodge numbers for the quotients of complete intersection Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant K\"ahler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, $G$, that arise in the classification are either $Z_2$ or contain $Z_4$, $Z_2 \times Z_2$, $Z_3$ or $Z_5$ as a subgroup. The Hodge numbers for the quotients for which the group $G$ contains $Z_3$ or $Z_5$ have been computed previously. This paper deals with the remaining cases, for which $G \supseteq Z_4$ or $G\supseteq Z_2 \times Z_2$. We also compute the Hodge numbers for 99 of the 166 CICY's which have $Z_2$ quotients.