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PreprintarXiv licencearXiv

The F-signature of Determinantal Rings

  • Hang Huang
  • Cheng Meng
  • Suchitra Pande
  • Yevgeniya Tarasova
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Abstract

Let Rn,p be the determinantal hypersurface ring defined by the determinant of a generic n × n matrix in characteristic p where n ≥ 2. In this paper, we obtain explicit bounds for the F-signature of Rn,p. For the upper bound, we prove that this F-signature is decreasing in n, so the F-signature of R2,p serves as an upper bound, which is 2/3. For the lower bound, we find a toric degeneration Bn of Rn,p, so the F-signature of Bn serves as a lower bound. This F-signature can be computed using either Gröbner basis or Han-Monsky machinery, and its value is (n!)2/((2n−1)!).

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Cite

BibTeXRIS
BibTeX
@misc{huang2026fsignature,
  title = {{The F-signature of Determinantal Rings}},
  author = {Hang Huang and Cheng Meng and Suchitra Pande and Yevgeniya Tarasova},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32955},
  eprint = {2609.32955},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32955},
}
RIS
TY  - UNPB
TI  - The F-signature of Determinantal Rings
AU  - Hang Huang
AU  - Cheng Meng
AU  - Suchitra Pande
AU  - Yevgeniya Tarasova
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32955
UR  - https://arxiv.org/abs/2609.32955
AB  - Let R_n,p be the determinantal hypersurface ring defined by the determinant of a generic n × n matrix in characteristic p where n ≥ 2. In this paper, we obtain explicit bounds for the F-signature of R_n,p. For the upper bound, we prove that this F-signature is decreasing in n, so the F-signature of R_2,p serves as an upper bound, which is 2/3. For the lower bound, we find a toric degeneration B_n of R_n,p, so the F-signature of B_n serves as a lower bound. This F-signature can be computed using either Gröbner basis or Han-Monsky machinery, and its value is (n!)^2/((2n−1)!).
ER  -