Ulrich subvarieties and the non-existence of low rank Ulrich bundles on complete intersections
Abstract
We characterize the existence of an Ulrich vector bundle on a variety X ⊂ P N X \subset \mathbb {P}^N in terms of the existence of a subvariety satisfying some precise conditions. Then we use this fact to prove that a complete intersection of dimension n ≥ 4 n \ge 4 , which if n = 4 n=4 is very general and not of type ( 2 , 2 ) (2,2) , does not carry any Ulrich bundles of rank r ≤ 3 r \le 3 unless n = 4 , r = 2 n=4, r=2 and X X is a quadric.
Fields of Study & Subjects
Commutative Algebra and Its Applications
Advanced Numerical Analysis Techniques
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Volume
- 379
- Issue
- 8
- Pages
- 5809–5846
- Publication date
- 14 April 2026
- Language
- EN