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Ulrich Bundles on certain Grassmann Bundles Over Curves
Abstract
Let E be a slope-semistable vector bundle on smooth projective curve C. Assume, $ π: G= Gr_{C}(r, E) \to C$ denote the relative Grassmannian of rank r quotients of E. We prove that for every very ample polarization L= OG(1) ⊗ π* A the polarized variety (G,L) possess an Ulrich bundle. The construction globalizes homogeneous ulrich bundle on Grassmannian fibres. The remaining cohomology vanishing problem reduced to an acyclicity criterion on the base curve. We finally use Falting's cohomological charaterization of semistability.
Related
- Existence of Ulrich bundles on polarized surfaces and weakly Ulrich bundles on polarized varieties in positive characteristic
- On the existence of smooth varieties of any dimension carrying no Ulrich bundles for some very ample line bundle
- Ulrich bundles on intersections of two quadrics
- On the classification of polarized surfaces with weakly Ulrich or initialized aCM tangent bundles
- On the existence of polarized varieties without weakly Ulrich bundles
BibTeX
@misc{saha2026ulrich,
title = {{Ulrich Bundles on certain Grassmann Bundles Over Curves}},
author = {Arunima Saha and Anindya Mukherjee and Pabitra Barik},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15068},
eprint = {2609.15068},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15068},
}
RIS
TY - UNPB
TI - Ulrich Bundles on certain Grassmann Bundles Over Curves
AU - Arunima Saha
AU - Anindya Mukherjee
AU - Pabitra Barik
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15068
UR - https://arxiv.org/abs/2609.15068
AB - Let E be a slope-semistable vector bundle on smooth projective curve C. Assume, $ π: G= Gr_{C}(r, E) \to C$ denote the relative Grassmannian of rank r quotients of E. We prove that for every very ample polarization L= O_G(1) ⊗ π^* A the polarized variety (G,L) possess an Ulrich bundle. The construction globalizes homogeneous ulrich bundle on Grassmannian fibres. The remaining cohomology vanishing problem reduced to an acyclicity criterion on the base curve. We finally use Falting's cohomological charaterization of semistability.
ER -