PreprintCC BY 4.0arXiv
Ulrich bundles on intersections of two quadrics
Abstract
We construct Ulrich bundles on smooth intersections of two quadrics. We determine all possible ranks and prove the existence of indecomposable Ulrich bundles of every allowable rank. To our knowledge, this gives the first such construction for a family of nonhomogeneous varieties of arbitrarily large dimension. We also study the moduli spaces of these bundles and relate them to moduli spaces of vector bundles on curves. For intersections of two even-dimensional quadrics, our results prove a conjecture of Eisenbud and Schreyer.
Related
- Motivic classes of Fano schemes of lines on intersections of two quadrics
- Existence of Ulrich bundles on polarized surfaces and weakly Ulrich bundles on polarized varieties in positive characteristic
- Ulrich Bundles on certain Grassmann Bundles Over Curves
- On the existence of smooth varieties of any dimension carrying no Ulrich bundles for some very ample line bundle
- Fundamental groups of complements of wobbly divisors in intersections of two quadrics
BibTeX
@misc{jung2026ulrich,
title = {{Ulrich bundles on intersections of two quadrics}},
author = {Jiwan Jung and Kyoung-Seog Lee and Han-Bom Moon},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09596},
eprint = {2609.09596},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09596},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Ulrich bundles on intersections of two quadrics
AU - Jiwan Jung
AU - Kyoung-Seog Lee
AU - Han-Bom Moon
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09596
UR - https://arxiv.org/abs/2609.09596
AB - We construct Ulrich bundles on smooth intersections of two quadrics. We determine all possible ranks and prove the existence of indecomposable Ulrich bundles of every allowable rank. To our knowledge, this gives the first such construction for a family of nonhomogeneous varieties of arbitrarily large dimension. We also study the moduli spaces of these bundles and relate them to moduli spaces of vector bundles on curves. For intersections of two even-dimensional quadrics, our results prove a conjecture of Eisenbud and Schreyer.
ER -