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PreprintarXiv licencearXiv

Uniform non-homogeneous vector bundles: A counterexample to the conjecture of Drézet and Ballico-Ellia

  • Graham Denham
  • Rosa Miró-Roig
  • Hal Schenck
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Abstract

We construct a rank-9 uniform non-homogeneous vector bundle on ℙ5. This yields the first counterexample to the longstanding open conjecture that every uniform vector bundle of rank r<2n on ℙn is homogeneous.

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Cite

BibTeXRIS
BibTeX
@misc{denham2026uniform,
  title = {{Uniform non-homogeneous vector bundles: A counterexample to the conjecture of Drézet and Ballico-Ellia}},
  author = {Graham Denham and Rosa Miró-Roig and Hal Schenck},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20208},
  eprint = {2610.20208},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20208},
}
RIS
TY  - UNPB
TI  - Uniform non-homogeneous vector bundles: A counterexample to the conjecture of Drézet and Ballico-Ellia
AU  - Graham Denham
AU  - Rosa Miró-Roig
AU  - Hal Schenck
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20208
UR  - https://arxiv.org/abs/2610.20208
AB  - We construct a rank-9 uniform non-homogeneous vector bundle on ℙ^5. This yields the first counterexample to the longstanding open conjecture that every uniform vector bundle of rank r<2n on ℙ^n is homogeneous.
ER  -