Finding equations of the fake projective plane $(C18,p=3,\{2I\})$

Lev Borisov; Bojue Wang

Finding equations of the fake projective plane $(C18,p=3,\{2I\})$

Algebraic Geometry 2025-12-04 v1

Authors: Lev Borisov , Bojue Wang

Abstract

We find explicit equations of a new pair of fake projective planes, labeled by $(C18,p=3,\{2I\})$ in the Cartwright-Steger classification. Our method involves starting with known equations of a commensurable fake projective plane $(C18,p=3,\emptyset,d_3 D_3)$ and working through a chain of cyclic covers and quotients to get to the new one.

Keywords

fake projective planes algebraic geometry cyclic covers quotients Cartwright-Steger classification explicit equations

Cite

@article{arxiv.2512.03213,
  title  = {Finding equations of the fake projective plane $(C18,p=3,\{2I\})$},
  author = {Lev Borisov and Bojue Wang},
  journal= {arXiv preprint arXiv:2512.03213},
  year   = {2025}
}

Comments

16 pages + auxiliary files

Finding equations of the fake projective plane $(C18,p=3,\{2I\})$

Abstract

Keywords

Cite

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