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PreprintarXiv licencearXiv

Quadratic and Koszul Licci Ideals

  • Paolo Mantero
  • Matthew Mastroeni
  • Jason McCullough
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Abstract

We give a complete classification of all Koszul licci ideals, including a complete description of the defining equations and graded Betti tables for these ideals, showing that they exactly correspond to quadratic licci ideals that are at most two links away from a complete intersection. More generally, we show how to uniquely associate the Hilbert function of a quadratic licci ideal to a partition of its codimension, and use it to prove that the Hilbert function of a quadratic ideal determines whether or not it is licci. This provides a strong affirmative answer in the quadratic case to a question of Huneke, Polini, and Ulrich asking whether graded Betti tables determine the licci property of graded ideals.

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Cite

BibTeXRIS
BibTeX
@misc{mantero2026quadratic,
  title = {{Quadratic and Koszul Licci Ideals}},
  author = {Paolo Mantero and Matthew Mastroeni and Jason McCullough},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01224},
  eprint = {2611.01224},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01224},
}
RIS
TY  - UNPB
TI  - Quadratic and Koszul Licci Ideals
AU  - Paolo Mantero
AU  - Matthew Mastroeni
AU  - Jason McCullough
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01224
UR  - https://arxiv.org/abs/2611.01224
AB  - We give a complete classification of all Koszul licci ideals, including a complete description of the defining equations and graded Betti tables for these ideals, showing that they exactly correspond to quadratic licci ideals that are at most two links away from a complete intersection. More generally, we show how to uniquely associate the Hilbert function of a quadratic licci ideal to a partition of its codimension, and use it to prove that the Hilbert function of a quadratic ideal determines whether or not it is licci. This provides a strong affirmative answer in the quadratic case to a question of Huneke, Polini, and Ulrich asking whether graded Betti tables determine the licci property of graded ideals.
ER  -