PreprintarXiv licencearXiv
On the existence of smooth varieties of any dimension carrying no Ulrich bundles for some very ample line bundle
Abstract
Using some recent examples of Anghel in dimension $2$, we prove that for any n ≥ 3 there exist many smooth n-dimensional varieties X with a very ample line bundle H, such that there is no Ulrich bundle for (X,H). Moreover, we find many new examples in dimension $2$.
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BibTeX
@misc{lopez2026existence,
title = {{On the existence of smooth varieties of any dimension carrying no Ulrich bundles for some very ample line bundle}},
author = {Angelo Felice Lopez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06678},
eprint = {2609.06678},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06678},
}
RIS
TY - UNPB
TI - On the existence of smooth varieties of any dimension carrying no Ulrich bundles for some very ample line bundle
AU - Angelo Felice Lopez
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.06678
UR - https://arxiv.org/abs/2609.06678
AB - Using some recent examples of Anghel in dimension $2$, we prove that for any n ≥ 3 there exist many smooth n-dimensional varieties X with a very ample line bundle H, such that there is no Ulrich bundle for (X,H). Moreover, we find many new examples in dimension $2$.
ER -