PreprintarXiv licencearXiv
On the existence of polarized varieties without weakly Ulrich bundles
Abstract
We give an obstruction to the existence of bundles ℰ on a smooth n-dimensional polarized variety such that ℰ is a-regular and ℰ*(KX+(n+1)H) is b-regular. In particular, this gives an obstruction to the existence of weakly Ulrich bundles. Using these obstructions and some recent examples of \cite{a1} in dimension $2$, we prove that for any n ≥ 2 there exist many smooth n-dimensional varieties X with a very ample line bundle H, such that there is no weakly Ulrich bundle for (X,H), no ordinary instanton bundle with bounded quantum number, no non-ordinary μ-semistable instanton bundle with bounded quantum number and no bundle with supernatural cohomology and bounded roots.
Related
- Existence of Ulrich bundles on polarized surfaces and weakly Ulrich bundles on polarized varieties in positive characteristic
- Polarized varieties without arithmetically Cohen-Macaulay bundles and section rings without graded maximal Cohen-Macaulay modules in characteristic zero
- On the classification of polarized surfaces with weakly Ulrich or initialized aCM tangent bundles
- On the existence of smooth varieties of any dimension carrying no Ulrich bundles for some very ample line bundle
- Varieties Admitting Polarized Galois Endomorphisms
BibTeX
@misc{genc2026existence,
title = {{On the existence of polarized varieties without weakly Ulrich bundles}},
author = {Ozhan Genc and Angelo Felice Lopez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36231},
eprint = {2610.36231},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36231},
}
RIS
TY - UNPB
TI - On the existence of polarized varieties without weakly Ulrich bundles
AU - Ozhan Genc
AU - Angelo Felice Lopez
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36231
UR - https://arxiv.org/abs/2610.36231
AB - We give an obstruction to the existence of bundles ℰ on a smooth n-dimensional polarized variety such that ℰ is a-regular and ℰ^*(K_X+(n+1)H) is b-regular. In particular, this gives an obstruction to the existence of weakly Ulrich bundles. Using these obstructions and some recent examples of \cite{a1} in dimension $2$, we prove that for any n ≥ 2 there exist many smooth n-dimensional varieties X with a very ample line bundle H, such that there is no weakly Ulrich bundle for (X,H), no ordinary instanton bundle with bounded quantum number, no non-ordinary μ-semistable instanton bundle with bounded quantum number and no bundle with supernatural cohomology and bounded roots.
ER -