Related papers: Enriques manifolds

With any hyper-K\"ahler variety $K$ of generalized Kummer type is associated via Hodge theory a K3 surface $S_K$. We show how they are related geometrically through a moduli space of sheaves on $S_K$. As a consequence, building…

The main purpose in this paper is to study exceptional vector bundles on Enriques surfaces.

We study groups of bimeromorphic and biholomorphic automorphisms of projective hyperk\"ahler manifolds. Using an action of these groups on some non-positively curved space, we deduce many of their properties, including finite presentation,…

We give an elementary introduction to hyperk\"ahler manifolds, survey some of their interesting properties and some open problems.

Hyperelliptic manifolds are natural generalizations of hyperelliptic surfaces in dimensions. We provide a full classification of the groups, which arise as the holonomy group of a 4-dimensional hyperelliptic manifold. The classification is…

In this paper, we explore different possible choices of expanded degenerations and define appropriate stability conditions in order to construct good degenerations of Hilbert schemes of points over semistable degenerations of surfaces,…

We simplify the usual statement of the Torelli theorem for complex Enriques surfaces, by means of a lattice-theoretic trick. This allows easy proofs of several known results, which previously required intricate arithmetic arguments. The…

We construct K\"ahler groups with arbitrary finiteness properties by mapping products of closed Riemann surfaces holomorphically onto an elliptic curve: for each $r\geq 3$, we obtain large classes of K\"ahler groups that have classifying…

In this paper, we give three bases for the cohomology groups of the Hilbert scheme of two points on projective space. Then, we use these bases to compute all effective and nef cones of higher codimensional cycles on the Hilbert scheme.…

We prove a generalization of Hsiung-Minkowski formulas for closed submanifolds in semi-Riemannian manifolds with constant curvature. As a corollary, we obtain volume and area upper bounds for k-convex hypersurfaces in terms of a weighted…

We show that the general Enriques surface can be recovered from the Kuznetsov component of its bounded derived category of coherent sheaves.

We use vector-bundle techniques in order to compute $\dim W^1_d(C)$ where $C$ is general and smooth in a linear system on an unnodal Enriques surface. We furthermore find new examples of smooth curves on Enriques surfaces with an infinite…

These are notes of my lectures given at the school on intersection theory and moduli at the ICTP, Trieste. We construct moduli spaces of K3 surfaces and higherdimensional hyperkaehler manifolds, including moduli spaces of (2,2)-conformal…

In the physicist's language, a brane in a hyperkahler manifold is a submanifold which is either complex or lagrangian with respect to three Kahler structures of the ambient manifold. By considering the fixed loci of certain involutions,…

We give a numerical criterion for the Nielsen realization problem for Enriques manifolds, based on the recent developments on the Birman-Hilden theory for hyper-K\"ahler manifolds and on Nielsen realization for hyper-K\"ahler manifolds. We…

We develop a Hilbert space framework for a number of general multi-scale problems from dynamics. The aim is to identify a spectral theory for a class of systems based on iterations of a non-invertible endomorphism. We are motivated by the…

We study semistable pairs on elliptic K3 surfaces with a section: we construct a family of moduli spaces of pairs, related by wall crossing phenomena, which can be studied to describe the birational correspondence between moduli spaces of…

We extend calculus from smooth manifolds to topological manifolds making use of a theory of generalized functions developed for this aim. Actually such extension fits into a boarder context: the universal construction of a site containing…

We show how one can construct new autoequivalences of some Calabi-Yau and hyperk"ahler varieties by passing from a smooth projective surface to the associated Hilbert scheme of points.

This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…