Related papers: Wall divisors on irreducible symplectic orbifolds …

Rational curves on Hilbert schemes of points on $K3$ surfaces and generalised Kummer manifolds are constructed by using Brill-Noether theory on nodal curves on the underlying surface. It turns out that all wall divisors can be obtained, up…

We study projective fourfolds of $K3^{[2]}$-type with a symplectic involution and the deformations of their quotients, called orbifolds of Nikulin types; they are IHS orbifolds. We compute the Riemann--Roch formula for Weil divisors on such…

We give a characterization of irreducible symplectic fourfolds which are given as Hilbert scheme of points on a K3 surface.

Nikulin-type orbifolds are certain singular 4-dimensional irreducible holomorphic symplectic varieties. We show that the monodromy group of Nikulin-type orbifolds is maximal and classify finite order symplectic automorphisms up to…

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a $K3$ surface and admitting a non-symplectic involution. We classify the possible discriminant forms of the invariant and…

We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C^2/G], respectively the singular quotient surface C^2/G, where G is a finite subgroup of SL(2,C) of type A or D. We give a decomposition of the…

Reflection walls of certain primitive vectors in the anti-invariant sublattice of the K3 lattice define Heegner divisors in the period space of Enriques surfaces. We show that depending on the norm of these primitive vectors, these Heegner…

We construct a new autoequivalence of the derived category of the Hilbert scheme of n points on a K3 surface, and of the variety of lines on a smooth cubic 4-fold. For Hilb^2 and the variety of lines, we use the theory of spherical…

A $K3$ 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 generic couple $(X,H)$ with $X$ a deformation of $(K3)^{[n]}$ and…

Let $X$ be a projective irreducible holomorphic symplectic manifold. We associate with any big $\mathbf{R}$-divisor $D$ on $X$ a convex polygon $\Delta_E^{\mathrm{num}}(D)$ of dimension 2, whose Euclidean volume is…

Under some conditions on the deformation type, which we expect to be satisfied for arbitrary irreducible symplectic varieties, we describe which big and nef line bundles on irreducible symplectic varieties have base divisors. In particular,…

We study the maps induced on cohomology by a Nikulin (i.e. a symplectic) involution on a K3 surface. We parametrize the eleven dimensional irreducible components of the moduli space of algebraic K3 surfaces with a Nikulin involution and we…

As their smooth analogue the irreducible symplectic varieties appear as elementary bricks in the generalizations of the Bogomolov decomposition theorem (arXiv:math/0402243, arXiv:2012.00441). Let $S$ be a K3 surface; generalizing the Fujiki…

Let X be a Hyperk\"{a}hler variety deformation equivalent to the Hilbert square on a K3 surface and let f be an involution preserving the symplectic form. We prove that the fixed locus of f consists of 28 isolated points and 1 K3 surface,…

We give a new proof for the maximality of the monodromy group of a Nikulin orbifold, a symplectic orbifold arising as terminalisation of a symplectic quotient of a $K3^{[2]}$-type fourfold.

First steps towards a classification of irreducible symplectic 4-folds whose integral 2-cohomology with 4-tuple cup product is isomorphic to that of Hilb^2(K3). We prove that any such 4-fold deforms to an irreducible symplectic 4-fold of…

Irreducible symplectic manifolds are one of the three building blocks of compact K\"ahler manifolds with numerically trivial canonical bundle by the Beauville-Bogomolov decomposition theorem. There are several singular analogues of…

There is two group actions on the Fano scheme of lines such that the quotient becomes an irreducible symplectic manifold. We showed that both quotients are birational to the generalized Kummer variety or the 2-points Hilbert scheme of a K3…

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…

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…