On Ulrich bundles on projective bundles

Andreas Hochenegger

doi:10.1007/s13366-021-00586-z

On Ulrich bundles on projective bundles

Algebraic Geometry 2025-03-04 v4

Authors: Andreas Hochenegger

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Abstract

In this article, the existence of Ulrich bundles on projective bundles $\mathbb P(E) \to X$ is discussed. In the case, that the base variety $X$ is a curve or surface, a close relationship between Ulrich bundles on $X$ and those on $\mathbb P(E)$ is established for specific polarisations. This yields the existence of Ulrich bundles on a wide range of projective bundles over curves and surfaces.

Keywords

ulrich bundles projective bundles polarisations algebraic curves algebraic surfaces vector bundles

Cite

@article{arxiv.2006.16553,
  title  = {On Ulrich bundles on projective bundles},
  author = {Andreas Hochenegger},
  journal= {arXiv preprint arXiv:2006.16553},
  year   = {2025}
}

Comments

15 pages. Same content as published version. There is an error in Proposition 5.13, added an erratum which will be published (separately) in Betr\"age zur Algebra und Geometrie (doi:10.1007/s13366-025-00786-x)

On Ulrich bundles on projective bundles

Abstract

Keywords

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