Work

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

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.01957

Author: Aleshin, Sergei

Institution: Institute for Information Transmission Problems

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Ministry of Science and Higher Education of the Russian Federation, Institute for Information and Communications Technology Promotion

OpenAlex ID: W7216233609

Cites: 6

Cited by:

Related to: 10