Hodge numbers for CICYs with symmetries of order 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 Kähler 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 × 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 ⊇ Z 4 or G ⊇ Z 2 × Z 2 . We also compute the Hodge numbers for 99 of the 166 CICY's which have Z 2 quotients.

Fibrations in non-simply connected Calabi-Yau quotients

“…For odd dimensional cases, non-simply connected Calabi-Yau manifolds can be obtained from this construction by quotienting by an appropriate freely acting symmetry. Those freely acting symmetries which descend from a linear action on the homogeneous coordinates of the ambient spaces in the original CICY list of 7,890 matrices, and for which the symmetry restricted defining relation still generically leads to a smooth Calabi-Yau three-fold, have been classified in [21] (see [30][31][32][33][34] for studies of the properties of these manifolds).…”

“…For example, applying this to the holomorphic tangent bundle V = T X yields the Hodge numbers of X. The Hodge numbers of the CICY quotients of the form described above were calculated in [30][31][32][33][34]. Chern classes have the following simple property under pull-back maps…”

Hodge numbers for all CICY quotients

“…The present work concludes and completes the series of papers [43][44][45] whose purpose is the computation of Hodge numbers for smooth quotients of CICY manifolds. Our results are summarised in Figure 1.…”

Getting CICY high

“…The Euler character is a cubic expression in the elements of the configuration matrix. Calculating h 1,1 and h 2,1 is conceptually straightforward but requires some care [39][40][41][42][43][44]. One of the goals of applying machine learning to this dataset is to circumvent the necessity of studious sequence chasing.…”