We analyze the relationship between abelian fourfolds of Weil type and Hodge structures of type K3, and we extend some of these correspondences to the case of arbitrary dimension.

The study of moduli spaces by means of the period mapping has found its greatest success for moduli spaces of varieties with trivial canonical bundle, or more generally, varieties with Kodaira dimension zero. Now these moduli spaces play a pivotal rôle in the classification theory of algebraic varieties, since varieties with nonnegative Kodaira dimension which are not of general type admit bira...

We construct 16 reflection groups Γ acting on symmetric domains $\mathcal {D}$ of Cartan type IV, for which the graded algebras modular forms are freely generated by same weight, and in particular Satake-Baily-Borel compactification {D}/ {\Gamma }$ is isomorphic to a projective space. Four these previously known results Freitag-Salvati Manni, Matsumoto, Perna Runge. In addition we find several ...

ROBERT A. WOLAK In Chis short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation or equivalently the space of leaves of such a foliation is a Satake manifold . A particular attention is paid to transversely affine foliations . We present several conditions such ensure completeness of these foliations . In this short note...

is biholomorphic equivalent to the Satake compactification of H2/Γ′ for a certain subgroup Γ′ ⊂ Sp(2, Z). This variety has 96 singularities which correspond to certain zero-dimensional cusps and these singularities are ordinary double points (nodes). In the paper [CM] it has been pointed out that the results of [GN] imply that a (projective) small resolution of this variety is a rigid Calabi-Ya...