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PreprintCC BY 4.0arXiv

Explicit equations of three pairs of fake projective planes

  • Lev Borisov
  • Nathan Mann
Open at sourcePDFDOICite

Abstract

We find explicit polynomial equations in their bicanonical embeddings into ℂℙ9 for the pairs of fake projective planes labeled by (C18,p=3,{2},D3), (C18,p=3,{2},(dD)3) and (C18,p=3,{2},(d2D)3) in the Cartwright-Steger classification. We do this by starting with the equations of the commensurable fake projective plane labeled by (C18,p=3,{2I}) that were found in arXiv:2512.03213.

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Cite

BibTeXRIS
BibTeX
@misc{borisov2026explicit,
  title = {{Explicit equations of three pairs of fake projective planes}},
  author = {Lev Borisov and Nathan Mann},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33823},
  eprint = {2610.33823},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33823},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Explicit equations of three pairs of fake projective planes
AU  - Lev Borisov
AU  - Nathan Mann
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33823
UR  - https://arxiv.org/abs/2610.33823
AB  - We find explicit polynomial equations in their bicanonical embeddings into ℂℙ^9 for the pairs of fake projective planes labeled by (C18,p=3,{2},D_3), (C18,p=3,{2},(dD)_3) and (C18,p=3,{2},(d^2D)_3) in the Cartwright-Steger classification. We do this by starting with the equations of the commensurable fake projective plane labeled by (C18,p=3,{2I}) that were found in arXiv:2512.03213.
ER  -