Projective manifolds whose tangent bundle is Ulrich

Abstract

In this article, we give numerical restrictions on the Chern classes of Ulrich bundles on higher-dimensional manifolds, which are inspired by the results of Casnati in the case of surfaces. As a by-product, we prove that the only projective manifolds whose tangent bundle is Ulrich are the twisted cubic and the Veronese surface. Moreover, we prove that the cotangent bundle is never Ulrich.

arXiv commentwith an Appendix by Vladimiro Benedetti. 19 pages. Comments are welcome! v2: minor modifications