Related papers: Induced birational transformations on O'Grady's si…

We give a complete classification of symplectic birational involutions of manifolds of $OG10$ type. We approach this classification with three techniques -- via involutions of the Leech lattice, via involutions of cubic fourfolds and…

We describe here a degeneration of the symplectic desingularization of the moduli spaces of topologically trivial $GL(2,\mathbb{C})$ and $SL(2,\mathbb{C})$-Higgs bundles over a hyperelliptic curve, into O'Grady's ten and six dimensional…

We define a determinant on the group of automorphisms of non-trivial Severi-Brauer surfaces over a perfect field. Using the generators and relations, we extend this determinant to birational maps between Severi-Brauer surfaces. Using this…

We classify nonsymplectic automorphisms of prime order on irreducible holomorphic symplectic manifolds of O'Grady's 6-dimensional defamation type. More precisely, we give a classification of the invariant and coinvariant sublattices of the…

We classify finite groups that act faithfully by symplectic birational transformations on an irreducible holomorphic symplectic (IHS) manifold of OG10 type. In particular, if X is an IHS manifold of OG10 type and G a finite subgroup of…

In this paper we study equivariant moduli spaces of sheaves on a $ K3 $ surface $ X $ under a symplectic action of a finite group. We prove that under some mild conditions, equivariant moduli spaces of sheaves on $ X $ are irreducible…

For $S$ a very general polarized K3 surface of degree $8n-6$, we describe in geometrical terms a birational involution of the Hilbert scheme $S^{[n]}$ of $n$ points on the surface, whose existence was established from lattice theoretical…

Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces…

We study the existence of ample uniruled divisors on irreducible holomorphic symplectic manifolds that are deformation of the ten dimensional example introduced by O'Grady. In particular, we show that for any polarized OG10 manifold lying…

We give some examples of isomorphisms of moduli of sheaves induced by Fourier-Mukai functor. As applications, we give another proof on deformation type of some moduli spaces of sheaves on abelian and K3 surfaces.

In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.

A function from configuration space to moduli space of surface may induce a homomorphism between their fundamental groups which are braid groups and mapping class groups of surface, respectively. This map $\phi: B_k \rightarrow…

For any finite abelian group G, we study the moduli space of abelian $G$-covers of elliptic curves, in particular identifying the irreducible components of the moduli space. We prove that, in the totally ramified case, the moduli space has…

We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of…

We prove that any symplectic automorphism of finite order of an irreducible holomorphic symplectic manifold of O'Grady's 10-dimensional deformation type is trivial.

We study the geometry of some moduli spaces of twisted sheaves on K3 surfaces. In particular we introduce induced automorphisms from a K3 surface on moduli spaces of twisted sheaves on this K3 surface. As an application we prove the…

In the prequel to this paper, two versions of Le Potier's strange duality conjecture for sheaves over abelian surfaces were studied. A third version is considered here. In the current setup, the isomorphism involves moduli spaces of sheaves…

We prove that projective hyperk\"{a}hler manifolds of K3$^{[n]}$-type admitting a non-trivial symplectic birational self-map of finite order are isomorphic to moduli spaces of stable (twisted) coherent sheaves on K3 surfaces. Motivated by…

We give a lattice-theoretic classification of non-symplectic automorphisms of prime order of irreducible holomorphic symplectic manifolds of OG10 type. We determine which automorphisms are induced by a non-symplectic automorphism of prime…

Components of the Moduli space of sheaves on a K3 surface are parametrized by a lattice; the (algebraic) Mukai lattice. Isometries of the Mukai lattice often lift to symplectic birational isomorphisms of the collection of components. An…