Higher dimensional Calabi-Yau manifolds of Kummer type
Dominik Burek
TL;DR
This paper constructs higher-dimensional Calabi-Yau manifolds of Kummer type using elliptic curves with automorphisms, providing formulas for their Hodge numbers and generalizing previous results to arbitrary dimensions and characteristics.
Contribution
It introduces a new construction method for Calabi-Yau varieties of any dimension based on the Cynk-Hulek approach, expanding the class of known examples.
Findings
Constructed Calabi-Yau varieties of arbitrary dimensions
Derived formulas for Hodge numbers of these varieties
Extended results to Zariski properties in various characteristics
Abstract
Based on Cynk-Hulek method we construct complex Calabi-Yau varieties of arbitrary dimensions using elliptic curves with automorphism of order 6. Also we give formulas for Hodge numbers of varieties obtained from that construction. We shall generalize result of Katsura and Sch\"utt to obtain arbitrarily dimensional Calabi-Yau manifolds which are Zariski in any characteristic
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