Examples of non-rigid, modular vector bundles on hyperkähler manifolds

2023/02/17 by Enrico Fatighenti, Fatighenti, Enrico · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2302.09025

openalex publication_date 2023/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit examples of slope-stable and modular vector bundles on a hyperkähler manifold of K3^[2]-type which move in a 20-dimensional family and study their algebraic properties. These are obtained by performing standard linear algebra constructions on the examples studied by O'Grady of (rigid) modular bundles on the Fano varieties of lines of a general cubic 4-fold and the Debarre-Voisin hyperkähler manifold.

Cited by

• Higher discriminants of vector bundles and Schur functors

Related

• Rigid stable vector bundles on hyperkähler varieties of type K3^[n]
• Modular sheaves on hyperkähler varieties
• Modular vector bundles with and without moduli
• Rank 4 stable vector bundles on hyperkähler fourfolds of Kummer type
• O'Grady's tenfolds from stable bundles on hyper-Kähler fourfolds