On the classification of non-big Ulrich vector bundles on fourfolds

Angelo Felice Lopez; Roberto Muñoz; José Carlos Sierra

On the classification of non-big Ulrich vector bundles on fourfolds

Algebraic Geometry 2025-06-05 v3

Authors: Angelo Felice Lopez , Roberto Muñoz , José Carlos Sierra

Abstract

We give an almost complete classification of non-big Ulrich vector bundles on fourfolds. This allows to classify them in the case of Picard rank one fourfolds, of Mukai fourfolds and in the case of Del Pezzo $n$ -folds for $n \le 4$ . We also classify Ulrich bundles with non-big determinant on Del Pezzo and Mukai $n$ -folds, $n \ge 2$ .

Keywords

ulrich vector bundles fourfolds classification picard rank mukai fourfolds del pezzo varieties

Cite

@article{arxiv.2205.10143,
  title  = {On the classification of non-big Ulrich vector bundles on fourfolds},
  author = {Angelo Felice Lopez and Roberto Muñoz and José Carlos Sierra},
  journal= {arXiv preprint arXiv:2205.10143},
  year   = {2025}
}

Comments

The paper arXiv:2201.06019v1 has been split into two papers: arXiv:2201.06019v2 and the current paper. Together they supersede arXiv:2201.06019v1. v2: several changes according to referee's requests. Added two tables at the end of the paper. v3: corrected several typos

On the classification of non-big Ulrich vector bundles on fourfolds

Abstract

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