Limit F-invariants of the simple singularities and the Fermat hypersurfaces

@misc{castillorey2026limit,
  title = {{Limit F-invariants of the simple singularities and the Fermat hypersurfaces}},
  author = {Joel Castillo-Rey},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.39133},
  eprint = {2609.39133},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.39133},
}

TY  - UNPB
TI  - Limit F-invariants of the simple singularities and the Fermat hypersurfaces
AU  - Joel Castillo-Rey
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.39133
UR  - https://arxiv.org/abs/2609.39133
AB  - In this article, we compute the limit Hilbert--Kunz multiplicities and limit F-signatures of all the simple singularities and the Hilbert--Kunz multiplicities of the Fermat hypersurfaces, generalizing the well-known sec z + tan z formula by Gessel and Monsky for the A1 singularities, using the theory of h-functions. We also obtain a functional equation relating the phi-function of a hypersurface to its reflection. Using limit F-invariants, we generalize both a characterization of regular local rings through F-invariants and the known cases of the Watanabe--Yoshida conjecture to characteristic zero.
ER  -