Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 43 min ago
PreprintarXiv licencearXiv

Numerical invariants for three-generated ideals

  • Marcos Jardim
  • Felipe Monteiro
  • Abbas Nasrollah Nejad
  • Zaqueu Ramos
Open at sourcePDFDOICite

Abstract

We study numerical invariants of homogeneous ideals generated by three forms, with particular emphasis on the interaction between the initial degree of the syzygy module, the multiplicity of the codimension-two part of the ideal, and the Bourbaki degree. We extend the Bourbaki degree from gradient ideals of plane curves to arbitrary three-generated homogeneous ideals and obtain sharp numerical bounds in both the general and the equigenerated settings. In the equigenerated case, these bounds extend the du Plessis--Wall picture and lead to the study of numerical, structural, dimensional, and integrable gaps. We show that numerical admissibility does not in general imply realizability and obtain further restrictions from the minimal graded free resolution. As an application, we determine the possible Bourbaki degrees of reduced singular quartic plane curves and describe them in terms of their singularity configurations; the possible values are 0,1,2,3,4,6,7,8.

Related

  1. Geometry of three--generated ideals in the plane
    Felipe Monteiro
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Symbolic Powers and Asymptotic Invariants of GL-Invariant Ideals
    Sankhaneel Bisui, Alexandra Seceleanu
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. ASSOCIATED PRIMES, WITNESSES, AND OMEGA INVARIANTS OF MONOMIAL IDEALS
    Jacob Miller, Mehrdad Nasernejad, Ştefan O Tohǎneanu
    HALPreprintCC BY 4.0Full textAlgebra & number theoryHALarXiv
  4. Reflexive ideals of a numerical semigroup
    P. Campochiaro, M. D'Anna, P. A. Garcia-Sanchez
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Homological invariants of Edge Ideals associated to powers of cycles
    Shahnawaz Ahmad Rather, S. Pirzada, M. Aijaz
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{jardim2026numerical,
  title = {{Numerical invariants for three-generated ideals}},
  author = {Marcos Jardim and Felipe Monteiro and Abbas Nasrollah Nejad and Zaqueu Ramos},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12253},
  eprint = {2609.12253},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12253},
}
RIS
TY  - UNPB
TI  - Numerical invariants for three-generated ideals
AU  - Marcos Jardim
AU  - Felipe Monteiro
AU  - Abbas Nasrollah Nejad
AU  - Zaqueu Ramos
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.12253
UR  - https://arxiv.org/abs/2609.12253
AB  - We study numerical invariants of homogeneous ideals generated by three forms, with particular emphasis on the interaction between the initial degree of the syzygy module, the multiplicity of the codimension-two part of the ideal, and the Bourbaki degree. We extend the Bourbaki degree from gradient ideals of plane curves to arbitrary three-generated homogeneous ideals and obtain sharp numerical bounds in both the general and the equigenerated settings. In the equigenerated case, these bounds extend the du Plessis--Wall picture and lead to the study of numerical, structural, dimensional, and integrable gaps. We show that numerical admissibility does not in general imply realizability and obtain further restrictions from the minimal graded free resolution. As an application, we determine the possible Bourbaki degrees of reduced singular quartic plane curves and describe them in terms of their singularity configurations; the possible values are 0,1,2,3,4,6,7,8.
ER  -