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The Eisenbud-Huneke-Ulrich conjecture and bounds on minimal generators

  • Fuxiang Yang
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Abstract

We prove the Eisenbud--Ulrich conjecture on the powers of linearly presented ideals in characteristic zero. More generally, we study stabilization bounds for powers of m-primary ideals in a polynomial ring with partially linear resolutions, making further progress toward the more general Eisenbud--Huneke--Ulrich conjecture. We prove a global generation result on relevant higher syzygy bundles, which is a crucial ingredient to the proof of the Eisenbud--Ulrich conjecture. We also establish lower bounds for the number of minimal generators in two settings: ideals generated by quadrics and ideals that are virtually linearly presented. Motivated by these results, we formulate a conjecture predicting sharp lower bounds for the number of minimal generators of such ideals.

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Cite

BibTeXRIS
BibTeX
@misc{yang2026eisenbudhunekeulrich,
  title = {{The Eisenbud-Huneke-Ulrich conjecture and bounds on minimal generators}},
  author = {Fuxiang Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12302},
  eprint = {2609.12302},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12302},
}
RIS
TY  - UNPB
TI  - The Eisenbud-Huneke-Ulrich conjecture and bounds on minimal generators
AU  - Fuxiang Yang
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.12302
UR  - https://arxiv.org/abs/2609.12302
AB  - We prove the Eisenbud--Ulrich conjecture on the powers of linearly presented ideals in characteristic zero. More generally, we study stabilization bounds for powers of m-primary ideals in a polynomial ring with partially linear resolutions, making further progress toward the more general Eisenbud--Huneke--Ulrich conjecture. We prove a global generation result on relevant higher syzygy bundles, which is a crucial ingredient to the proof of the Eisenbud--Ulrich conjecture. We also establish lower bounds for the number of minimal generators in two settings: ideals generated by quadrics and ideals that are virtually linearly presented. Motivated by these results, we formulate a conjecture predicting sharp lower bounds for the number of minimal generators of such ideals.
ER  -