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PreprintarXiv licencearXiv

Herzog Class of Codimension $3$ Licci Monomial Ideals

  • Suhas Vadan Gondi
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Abstract

Let S be the polynomial ring in three variables with homogeneous maximal ideal m. Licci ideals are ideals that can be linked by a finite number of steps to a complete intersection. All licci ideals admit a rigid deformation, and two licci ideals are said to be in the same Herzog class if they have a common rigid deformation. Guerrieri-Ni-Weyman gave a parametrization for the Herzog classes of codimension $3$ licci ideals in terms of pairs of partitions associated to Schur functors. In this paper, we give an explicit formula that determines the Herzog class of a given m-primary licci monomial ideal.

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Cite

BibTeXRIS
BibTeX
@misc{gondi2026herzog,
  title = {{Herzog Class of Codimension $3$ Licci Monomial Ideals}},
  author = {Suhas Vadan Gondi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26010},
  eprint = {2610.26010},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26010},
}
RIS
TY  - UNPB
TI  - Herzog Class of Codimension $3$ Licci Monomial Ideals
AU  - Suhas Vadan Gondi
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26010
UR  - https://arxiv.org/abs/2610.26010
AB  - Let S be the polynomial ring in three variables with homogeneous maximal ideal m. Licci ideals are ideals that can be linked by a finite number of steps to a complete intersection. All licci ideals admit a rigid deformation, and two licci ideals are said to be in the same Herzog class if they have a common rigid deformation. Guerrieri-Ni-Weyman gave a parametrization for the Herzog classes of codimension $3$ licci ideals in terms of pairs of partitions associated to Schur functors. In this paper, we give an explicit formula that determines the Herzog class of a given m-primary licci monomial ideal.
ER  -