Examples of non-rigid, modular vector bundles on hyperk\"ahler manifolds

TL;DR

This paper presents examples of non-rigid, modular vector bundles on hyperk"ahler manifolds, expanding understanding of their algebraic properties and moduli spaces.

Contribution

It constructs new slope-stable, modular vector bundles on K3^{[2]}-type hyperk"ahler manifolds, derived from linear algebra operations on known examples.

Findings

Bundles form a 20-dimensional family

Bundles are slope-stable and modular

Examples extend known constructions to new settings

Abstract

We exhibit examples of slope-stable and modular vector bundles on a hyperk\"ahler 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 hyperk\"ahler manifold.