Related papers: Enriques manifolds

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…

This survey discusses hyperbolicity properties of moduli stacks and generalisations of the Shafarevich Hyperbolicity Conjecture to higher dimensions. It concentrates on methods and results that relate moduli theory with recent progress in…

We prove the existence of Ulrich sheaves on the Hilbert scheme of two points on a polarized K3 surface or an abelian surface. The construction proceeds by descending Ulrich bundles on the surface to the symmetric square and lifting them to…

We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each K-trivial surface, we write down a simple criterion ensuring that the tautological bundles are big and nef, and illustrate it by examples. In the…

We study the orbifold Hirzebruch-Riemann-Roch (HRR) theorem for quotient Deligne-Mumford stacks, explore its relation with the representation theory of finite groups, and derive a new orbifold HRR formula via an orbifold Mukai pairing. As a…

We prove that the moduli space of empty real Enriques surfaces (and, thus, the moduli space of compact orientable 4-dimensional Einstein manifolds whose universal covering is a K3-surface and \pi_1(E) = Z/2 x Z/2) is connected. The proof is…

In this paper, we show the moduli spaces of stable sheaves on K3 surfaces are irreducible symplectic manifolds, if the associated Mukai vectors are primitive. More precisely, we show that they are related to the Hilbert scheme of points. We…

We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…

We introduce an analogue in hyperkahler geometry of the symplectic implosion, in the case of SU(n) actions. Our space is a stratified hyperkahler space which can be defined in terms of quiver diagrams. It also has a description as a…

We prove the rationality of the coarse moduli spaces of Coble surfaces and of nodal Enriques surfaces over the field of complex numbers.

In this paper, we study the complex structures of complete hyperk\"ahler four-manifolds of infinite topological type arising from the Gibbons-Hawking ansatz. We show that for almost all complex structures in the hyperk\"ahler family, the…

We study the locus of smooth hypersurfaces inside the Hilbert scheme of a smooth projective complex variety. In the spirit of scanning, we construct a map to a continuous section space of a projective bundle, and show that it induces an…

Let $X\to C$ be an elliptic surface with integral fibers and a section. The Hilbert scheme $X^{[n]}$ fibers over $C^{[n]}$. We construct a commutative group scheme over the entire base $C^{[n]}$ that embeds as an open subscheme of the…

In this paper, we give the geometric meaning of hypersurfaces with constant mean curvature in a Finsler manifold by using volume preserving variation. Then we give the correspondence between principal curvatures of submanifolds by a…

We investigate compact Kahler manifolds, which are acted on by a semisimple compact Lie group G of isometries with one hypersurface orbit. In case of ordinary action and projectable complex structure, we set up a one to one correspondence…

Here we construct spaces of coinvariants for Heisenberg vertex algebras on abelian varieties and show that these globalize to twisted $\mathscr{D}$-modules on the moduli space of abelian varieties. Remarkably, we recover the standard…

We discuss some relations of moduli of sheaves on rational surfaces by using universal extensions. These are a generalization of Maruyama's method to construct Uhlenbeck compactification of moduli of vector bundles.

We study the cones of surfaces on varieties of lines on cubic fourfolds and Hilbert schemes of points on K3 surfaces. From this we obtain new examples of nef cycles which fail to be pseudoeffective.

In this paper we discuss the number of Enriques quotients of a fixed K3 surface. We prove the finiteness and unboundedness of the number. We also show an example of Kummer surface of product type where we can successfully classify all the…

Let $X$ be a projective K3 surfaces. In two examples where there exists a fine moduli space $M$ of stable vector bundles on $X$, isomorphic to a Hilbert scheme of points, we prove that the universal family $\mathcal{E}$ on $X\times M$ can…