16 citations · 75 across the 25 of their papers we have counts for
18 papers · 1 filter
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
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…
Some remarks on Brauer Classes of K3-type
Federica Galluzzi, Bert van Geemen
An element in the Brauer group of a general complex projective surface defines a sublattice of the transcendental lattice of . We consider those elements of prime order…
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…
On families of K3 surfaces with real multiplication
Bert van Geemen, Matthias Schütt
We exhibit large families of K3 surfaces with real multiplication, both abstractly using lattice theory, the Torelli theorem and the surjectivity of the period map, as well as expl…
Invariants of Vanishing Brauer Classes
Federica Galluzzi, Bert van Geemen
A specialization of a K3 surface with Picard rank one to a K3 with rank two defines a vanishing class of order two in the Brauer group of the general K3 surface. We give the B-fiel…
A Calabi-Yau threefold coming from two black holes
Dino Festi, Bert van Geemen
In this paper, we show that a set of six square roots of homogeneous polynomials in four variables, related to a binary system of black holes studied by Stefan Weinzierl, is not ra…
Weil Classes and Decomposable Abelian Fourfolds
Bert van Geemen
We determine which codimension two Hodge classes on , where is a general abelian surface, deform to Hodge classes on a family of abelian fourfolds of Weil type. If a…
Contractions of hyper-Kähler fourfolds and the Brauer group
Bert van Geemen, Grzegorz Kapustka
We study the geometry of exceptional loci of birational contractions of hyper-Kähler fourfolds that are of K3-type. These loci are conic bundles over K3 surfaces and we det…
A remark on generalized complete intersections
Alice Garbagnati, Bert van Geemen
We observe that an interesting method to produce non-complete intersection subvarieties, the generalized complete intersections from L. Anderson and coworkers, can be understood an…
A very special EPW sextic and two IHS fourfolds
Maria Donten-Bury, Bert van Geemen, Grzegorz Kapustka +2
We show that the Hilbert scheme of two points on the Vinberg surface has a 2:1 map onto a very symmetric EPW sextic in . The fourfold is singular along $…
On a conjecture of Matsushita
Bert van Geemen, Claire Voisin
We prove a weak version of a conjecture of Matsushita saying that for a Lagrangian fibration on a hyper-Kaehler manifold , the moduli map for the fibers is either generically of…
Abelian surfaces with an automorphism and quaternionic multiplication
Matteo A. Bonfanti, Bert van Geemen
We construct one dimensional families of Abelian surfaces with quaternionic multiplication which also have an automorphism of order three or four. Using Barth's description of the…
A Picard modular fourfold and the Weyl group W(E_6)
Bert van Geemen, Kenji Koike
We study the geometry of a Picard modular fourfold which parametrizes abelian fourfolds of Weil type for the field of cube roots of unity. We find a projective model of this fourfo…
Some equations for the universal Kummer variety
Bert van Geemen
We give a method to find quartic Heisenberg invariant equations for Kummer varieties and we give some explicit examples. From these equations for g-dimensional Kummer varieties one…
Geometry and Arithmetic of Maschke's Calabi-Yau Threefold
Gilberto Bini, Bert van Geemen
Maschke's Calabi-Yau threefold is the double cover of projective three space branched along Maschke's octic surface. This surface is defined by the lowest degree invariant of a cer…
Two moduli spaces of abelian fourfolds with an automorphism of order five
Bert van Geemen, Matthias Schuett
We find explicit projective models of a compact Shimura curve and of a (non-compact) surface which are the moduli spaces of principally polarised abelian fourfolds with an automorp…
Examples of Calabi-Yau threefolds parametrised by Shimura varieties
Alice Garbagnati, Bert van Geemen
These are notes from talks of the authors on some explicit examples of families of Calabi-Yau threefolds which are parametrised by a Shimura variety. We briefly review the periods…