Towards a modular construction of OG10

TL;DR

This paper constructs a new stable hyperholomorphic vector bundle on hyper-K"ahler manifolds of -type, linking its moduli space to OG10, thus suggesting new pathways for generating hyper-K"ahler manifolds.

Contribution

It introduces the first example of such a vector bundle with a smooth deformation space, connecting moduli spaces of sheaves to OG10 hyper-K"ahler manifolds.

Findings

Constructed a stable hyperholomorphic vector bundle of rank five.

Proved the moduli space is birational to an OG10 hyper-Ke4hler manifold.

Provided evidence that sheaf moduli spaces can produce new hyper-Ke4hler examples.

Abstract

We construct the first example of a stable hyperholomorphic vector bundle of rank five on every hyper-K\"ahler manifold of $\mathrm{K3}^{[2]}$-type whose deformation space is smooth of dimension ten. Its moduli space is birational to a hyper-K\"ahler manifold of type OG10. This provides evidence for the expectation that moduli spaces of sheaves on a hyper-K\"ahler could lead to new examples of hyper-K\"ahler manifolds.