Related papers: Singular symplectic moduli spaces

We investigate the moduli spaces of one- and two-dimensional sheaves on projective K3 and abelian surfaces that are semistable with respect to a nongeneral ample divisor with regard to the symplectic resolvability. We can exclude the…

For any $n \ge 3$, we consider the moduli space $M_n$ of semistable sheaves with Mukai vector $2(1,0,1-n)$ on a K3 surface. The moduli space $M_n$ is singular and lacks a crepant resolution, but might still admit a categorical crepant one.…

The aim of this paper is to study the singularities of certain moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non--generic polarization, with respect…

Mukai proved that the moduli space of simple sheaves on a smooth projective K3 surface is symplectic, and in \cite{FM2} we gave two constructions allowing one to construct new locally closed Lagrangian/isotropic subspaces of the moduli from…

In this paper we complete the determination of the index of factoriality of moduli spaces of semistable sheaves on an abelian or projective K3 surface $S$. If $v=2w$ is a Mukai vector, $w$ is primitive, $w^{2}=2$ and $H$ is a generic…

We study the local structure of the singularity in the moduli space of sheaves on a K3 surface which has been resolved by K O'Grady in his construction of new examples of hyperkaehler manifolds. In particular, we identify the singularity…

Let M be the moduli space of semistable sheaves with Mukai vector 2v on an abelian or K3 surface where v is primitive such that <v,v>=2. We show that the blow-up of the reduced singular locus of M provides a symplectic resolution of…

In this paper we study moduli spaces of sheaves on an abelian or projective K3 surface. If $S$ is a K3, $v=2w$ is a Mukai vector on $S$, where $w$ is primitive and $w^{2}=2$, and $H$ is a $v-$generic polarization on $S$, then the moduli…

This article studies moduli spaces of Bridgeland semistable objects in the Kuznetsov component of a cubic fourfold that don't admit a symplectic resolution, i.e., moduli spaces of objects with non-primitve Mukai vector v=mv_0 that is not of…

We show that the moduli spaces of sheaves on a projective K3 surface are irreducible symplectic varieties, and that the same holds for the fibers of the Albanese map of moduli spaces of sheaves on an Abelian surface.

In this survey article we describe moduli spaces of simple, stable, and semistable sheaves on K3 surfaces, following the work of Mukai, O'Grady, Huybrechts, Yoshioka, and others. We also describe some recent developments, including…

This paper studies deformations and birational maps between singular moduli spaces of semistable sheaves with 2-divisible Mukai vectors on K3 surfaces. It is showed that under certain conditions, two such moduli spaces of the same dimension…

We consider the singuralities of 2-dimensional moduli spaces of semi-stable sheaves on K3 surfaces. We show that the moduli space is normal, in particular the singuralities are rational double points. We also describe the exceptional locus…

Moduli spaces of stably irreducible sheaves on Kodaira surfaces belong to the short list of examples of smooth and compact holomorphic symplectic manifolds, and it is not yet known how they fit into the classification of holomorphic…

Following Bayer and Macr\`{i}, we study the birational geometry of singular moduli spaces $M$ of sheaves on a K3 surface $X$ which admit symplectic resolutions. More precisely, we use the Bayer-Macr\`{i} map from the space of Bridgeland…

We view the moduli space of semistable sheaves on a K3 surface as a global quotient stack, and compute its cotangent complex in terms of the universal sheaf on the Quot scheme. Relevant facts on the classical and reduced Atiyah classes are…

We study moduli spaces of sheaves over non-projective K3 surfaces. More precisely, if $v=(r,\xi,a)$ is a Mukai vector on a K3 surface $S$ with $r$ prime to $\xi$ and $\omega$ is a "generic" K\"ahler class on $S$, we show that the moduli…

The aim of this work is to give a description of the locally trivial monodromy group of irreducible symplectic varieties arising from moduli spaces of semistable sheaves on Abelian surfaces with non-primitive Mukai vector. The outcome is…

Moduli spaces of semistable torsion-free sheaves on a K3 surface $X$ are often holomorphic symplectic varieties, deformation equivalent to a Hilbert scheme parametrizing zero-dimensional subschemes of $X$. In fact this should hold whenever…

We study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of 2d polarised (split type) symplectic manifolds…