2015/06/11 by Laura Costa, Costa, L., Rosa M. Miró‐Roig +1
Mathematics · #14F05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1506.03586
openalex publication_date 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let V be a K-vector space of dimension n+1. In this paper, we focus our attention into the existence of irreducible homogeneous Ulrich bundles on flag manifolds \FF(p, q,n) which parameterizes all chains of linear subspaces Lp ⊂ Lq ⊂ \PP(V) of dimension p< q, respectively. We determine all irreducible homogeneous Ulrich bundles on \FF(0,n-1,n) and we prove that there are exactly 2n-1. Similarly, we prove that \FF(0,n-2,n) and \FF(1,n-1,n) are also the support of irreducible homogeneous Ulrich bundles. On the other hand, we prove that \FF(0,1,n) do not support any irreducible homogeneous Ulrich bundle. We end posing a conjecture concerning the existence of irreducible homogeneous Ulrich bundles on \FF(p,q,n) in terms of p and q.