Non-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension

Angelo Felice Lopez; Roberto Muñoz; José Carlos Sierra

Non-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension

Algebraic Geometry 2023-07-11 v3

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

Abstract

On any smooth $n$ -dimensional variety we give a pretty precise picture of rank $r$ Ulrich vector bundles with numerical dimension at most $\frac{n}{2}+r-1$ . Also, we classify non-big Ulrich vector bundles on quadrics and on the Del Pezzo fourfold of degree $6$ .

Keywords

ulrich vector bundles non-big numerical dimension quadrics del pezzo fourfold classification

Cite

@article{arxiv.2201.06019,
  title  = {Non-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension},
  author = {Angelo Felice Lopez and Roberto Muñoz and José Carlos Sierra},
  journal= {arXiv preprint arXiv:2201.06019},
  year   = {2023}
}

Comments

The previous version of arXiv:2201.06019 has been split into two papers. This version supersedes the first part, the second part will appear soon. v3: a few small improvements, as suggested by anonymous referee

Non-big Ulrich bundles: the classification on quadrics and the case of small numerical dimension

Abstract

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