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Deterministic Determination of Axial Constants, Sectional Regularities and Annihilator Numbers

  • Amir Hashemi
  • Rozhin Sadr
  • Werner M. Seiler
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Abstract

Axial constants and sectional regularities are recently introduced invariants of homogeneous polynomial ideals that, like the already earlier introduced annihilator numbers, depend on generic choices of coordinates. We provide effective characterisations of the genericity underlying these invariants in terms of β-maximal position and strong stability. In particular, we show that β-maximal position suffices for determining generic annihilator numbers and sectional regularities, while its combination with strong stability yields corresponding results for axial constants. We also develop deterministic linear algebra procedures for detecting the required generic positions and for computing these invariants.

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Cite

BibTeXRIS
BibTeX
@misc{hashemi2026deterministic,
  title = {{Deterministic Determination of Axial Constants, Sectional Regularities and Annihilator Numbers}},
  author = {Amir Hashemi and Rozhin Sadr and Werner M. Seiler},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22251},
  eprint = {2610.22251},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22251},
}
RIS
TY  - UNPB
TI  - Deterministic Determination of Axial Constants, Sectional Regularities and Annihilator Numbers
AU  - Amir Hashemi
AU  - Rozhin Sadr
AU  - Werner M. Seiler
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22251
UR  - https://arxiv.org/abs/2610.22251
AB  - Axial constants and sectional regularities are recently introduced invariants of homogeneous polynomial ideals that, like the already earlier introduced annihilator numbers, depend on generic choices of coordinates. We provide effective characterisations of the genericity underlying these invariants in terms of β-maximal position and strong stability. In particular, we show that β-maximal position suffices for determining generic annihilator numbers and sectional regularities, while its combination with strong stability yields corresponding results for axial constants. We also develop deterministic linear algebra procedures for detecting the required generic positions and for computing these invariants.
ER  -