PreprintarXiv licencearXiv
On the classification of polarized surfaces with weakly Ulrich or initialized aCM tangent bundles
Abstract
Counterexamples to the Eisenbud-Schreyer conjecture on the existence of Ulrich bundles have appeared recently (see Anghel [A1] and the third author [Lo]). As weakly Ulrich bundles are a useful generalization of Ulrich ones, in this paper, we classify smooth surfaces S⊆ ℙN with weakly Ulrich tangent bundle. They are Del-Pezzo surfaces of degree at least 5 and we classify the possible embeddings. An interesting feature is the appearance of two infinite series of polarizations, which is quite different from the Ulrich case [BMPT, LR]. We also achieve the classification of surfaces with initialized aCM tangent bundles and, as a consequence, of surfaces with almost Ulrich tangent bundles.
Related
- Non-null ruled surfaces and pseudo hyper-dual tangent sphere bundles
- Existence of Ulrich bundles on polarized surfaces and weakly Ulrich bundles on polarized varieties in positive characteristic
- Tangent bundles of Quot schemes of vector bundles on curves
- Uniform RC-positivity of tangent bundles
- Positive mass and rigidity for asymptotically flat tangent bundles
BibTeX
@misc{bhattacharya2026classification,
title = {{On the classification of polarized surfaces with weakly Ulrich or initialized aCM tangent bundles}},
author = {Debojyoti Bhattacharya and Ozhan Genc and Angelo Felice Lopez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.04739},
eprint = {2610.04739},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.04739},
}
RIS
TY - UNPB
TI - On the classification of polarized surfaces with weakly Ulrich or initialized aCM tangent bundles
AU - Debojyoti Bhattacharya
AU - Ozhan Genc
AU - Angelo Felice Lopez
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.04739
UR - https://arxiv.org/abs/2610.04739
AB - Counterexamples to the Eisenbud-Schreyer conjecture on the existence of Ulrich bundles have appeared recently (see Anghel [A1] and the third author [Lo]). As weakly Ulrich bundles are a useful generalization of Ulrich ones, in this paper, we classify smooth surfaces S⊆ ℙ^N with weakly Ulrich tangent bundle. They are Del-Pezzo surfaces of degree at least 5 and we classify the possible embeddings. An interesting feature is the appearance of two infinite series of polarizations, which is quite different from the Ulrich case [BMPT, LR]. We also achieve the classification of surfaces with initialized aCM tangent bundles and, as a consequence, of surfaces with almost Ulrich tangent bundles.
ER -