# zbMATH — the first resource for mathematics

Hodge numbers for CICYs with symmetries of order divisible by 4. (English) Zbl 1339.14023
Summary: 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 $$\mathbb{Z}_2$$ or contain $$\mathbb{Z}_4$$, $$\mathbb{Z}_2 \times \mathbb{Z}_2$$, $$\mathbb{Z}_3$$ or $$\mathbb{Z}_5$$ as a subgroup. The Hodge numbers for the quotients for which the group $$G$$ contains $$\mathbb{Z}_3$$ or $$\mathbb{Z}_5$$ have been computed previously. This paper deals with the remaining cases, for which $$G \supseteq \mathbb{Z}_4$$ or $$G \supseteq \mathbb{Z}_2 \times \mathbb{Z}_2$$. We also compute the Hodge numbers for 99 of the 166 CICY’s which have $$\mathbb{Z}_2$$ quotients.

##### MSC:
 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 32Q15 Kähler manifolds 32G20 Period matrices, variation of Hodge structure; degenerations 58A14 Hodge theory in global analysis
Full Text: