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An Algorithm for Generating All Berglund-Hubsch-Type Calabi-Yau Orbifolds and Their Mirrors. Classification of Maximal Admissible Groups

  • Sergei Aleshin
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Abstract

In this paper, we present an algorithm for constructing all Calabi-Yau orbifolds and their mirror pairs associated with an arbitrary Berglund-Hubsch-type model, and prove its correctness. In particular, the proposed method yields explicit generators for the groups defining the corresponding orbifolds. The method for classifying maximal admissible groups is proposed. We illustrate the application of the classification approach to an arbitrary Fermat-type Calabi-Yau manifold. In addition, as an illustrative example, we classify all maximal admissible groups of Fermat-type Calabi-Yau threefolds.

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Cite

BibTeXRIS
BibTeX
@misc{aleshin2026algorithm,
  title = {{An Algorithm for Generating All Berglund-Hubsch-Type Calabi-Yau Orbifolds and Their Mirrors. Classification of Maximal Admissible Groups}},
  author = {Sergei Aleshin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01957},
  eprint = {2610.01957},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01957},
}
RIS
TY  - UNPB
TI  - An Algorithm for Generating All Berglund-Hubsch-Type Calabi-Yau Orbifolds and Their Mirrors. Classification of Maximal Admissible Groups
AU  - Sergei Aleshin
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.01957
UR  - https://arxiv.org/abs/2610.01957
AB  - In this paper, we present an algorithm for constructing all Calabi-Yau orbifolds and their mirror pairs associated with an arbitrary Berglund-Hubsch-type model, and prove its correctness. In particular, the proposed method yields explicit generators for the groups defining the corresponding orbifolds. The method for classifying maximal admissible groups is proposed. We illustrate the application of the classification approach to an arbitrary Fermat-type Calabi-Yau manifold. In addition, as an illustrative example, we classify all maximal admissible groups of Fermat-type Calabi-Yau threefolds.
ER  -