5 papers
Hyperkähler sixfolds, abelian fourfolds of Weil type and a Hodge class
Bert van Geemen, Antonio Rapagnetta
There are now several proofs of the Hodge conjecture for the general abelian fourfold of Weil type with trivial discriminant. This paper provides another one. The abelian fourfolds…
Non-projective K3 surfaces with real or Salem multiplication
Eva Bayer-Fluckiger, Bert van Geemen, Matthias Schütt +1
We determine the Hodge endomorphism algebras of non-projective complex K3 surfaces (and more generally, hyperkähler manifolds). We show that they are either totally real fields or…
K3 surfaces with real or complex multiplication
Eva Bayer-Fluckiger, Bert van Geemen, Matthias Schütt
Let be a totally real number field of degree and let be an integer. We show that if then there exists an -dimensional family of com…
The two extremal rays of some Hyper-Kähler fourfolds
Federica Galluzzi, Bert Van Geemen
We consider projective Hyper-Kähler manifolds of dimension four that are deformation equivalent to Hilbert squares of K3 surfaces. In case such a manifold admits a divisorial cont…
Line geometry of pairs of second-order Hamiltonian operators and quasilinear systems
Giorgio Gubbiotti, Bert van Geemen, Pierandrea Vergallo
We demonstrate that a pair consisting of a second-order homogeneous Hamiltonian structure in components and its associated system of conservation laws is in bijective correspon…