Kieran G. O'Grady

activity

20042026

collaborators

5 papers

math.AG2026

HK manifolds of Type $K 3^{[a^{2} + 1]}$ as moduli spaces of projective bundles on HK manifolds of Type $K 3^{[2]}$

Kieran G. O'Grady

We prove results on moduli spaces of slope stable bundles of projective spaces on a hyperkähler manifold of Type $K 3^{[2]}$ . Let $X$ be projective of Type $K 3^{[2]}$ and $h$ be a (…

math.AG2026

Moduli of sheaves on hyperkähler manifolds

Kieran G. O'Grady

We survey recent advances in the theory of moduli spaces of stable sheaves on hyperkähler manifolds of dimension greater than $2$ . We start by recalling the well-known theory in di…

math.AG2024

Modular sheaves with many moduli

Kieran G. O'Grady

We exhibit moduli spaces of slope stable vector bundles on general polarized HK varieties $(X, h)$ of type $K 3^{[2]}$ which have an irreducible component of dimension $2 a^{2} + 2$ , with…

math.AG2023

The geometry of antisymplectic involutions, II

Laure Flapan, Emanuele Macrì, Kieran G. O'Grady +1

We continue our study of fixed loci of antisymplectic involutions on projective hyper-Kähler manifolds of $K3^{[n]}$ -type induced by an ample class of square 2 in the Beau…

math.AG2004

Involutions and linear systems on holomorphic symplectic manifolds

Kieran G. O'Grady

A $K 3$ surface with an ample divisor of self-intersection 2 is a double cover of the plane branched over a sextic curve. We conjecture that a similar statement holds for the generi…

HK manifolds of Type K3[a2+1] as moduli spaces of projective bundles on HK manifolds of Type K3[2]

Moduli of sheaves on hyperkähler manifolds

Modular sheaves with many moduli

The geometry of antisymplectic involutions, II

Involutions and linear systems on holomorphic symplectic manifolds

HK manifolds of Type $K 3^{[a^{2} + 1]}$ as moduli spaces of projective bundles on HK manifolds of Type $K 3^{[2]}$