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Higher Dimensional Analogon of Borcea-Voisin Calabi-Yau Manifolds, Their Hodge Numbers and L-Functions

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Abstract

We construct a series of examples of Calabi-Yau manifolds in an arbitrary dimension and compute the main invariants. In particular, we give higher dimensional generalization of Borcea-Voisin Calabi-Yau threefolds. We give a method to compute a local zeta function using the Frobenius morphism for orbifold cohomology introduced by Rose. We compute Hodge numbers of the constructed examples using orbifold Chen-Ruan cohomology.

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Acknowledgements

This paper is a part of author’s PhD thesis. I am deeply grateful to my advisor Sławomir Cynk for his enormous help. I would like to thank Matthias Schütt for helpful suggestions and comments. The author is supported by the National Science Center of Poland grant no. 2019/33/N/ST1/01502 and National Science Center of Poland grant no. 2020/36/T/ST1/00265. The final part of this work was conducted during the stay at the Leibniz Universität in Hannover. I would like to thank the institute for hospitality. Finally I would like to thank the anonymous referee for remarks and advices that substantially improve the presentation of this paper.

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  1. Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348, Kraków, Poland

    Dominik Burek

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Communicated by E. Smith.

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Burek, D. Higher Dimensional Analogon of Borcea-Voisin Calabi-Yau Manifolds, Their Hodge Numbers and L-Functions. Commun. Math. Phys. 405, 100 (2024). https://doi.org/10.1007/s00220-024-04965-0

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