Projective manifolds whose tangent bundle is Ulrich

2021/08/31 by Vladimiro Benedetti, Benedetti, Vladimiro, Pedro Montero +5
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2108.13944

openalex publication_date 2021/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• An introduction to Ulrich bundles
• Some evidence for the existence of Ulrich bundles
• On the correspondence between Ulrich bundles and curves on surfaces
• On varieties with Ulrich twisted tangent bundles
• Stable Ulrich bundles on cubic fourfolds