Boundaries of cycle spaces and degenerating Hodge structures

Abstract

We study a property of cycle spaces in connection with degenerating Hodge structures of odd-weight, and we construct maps from some partial compactifications of period domains to the Satake compatifications of Siegel spaces. These maps are a generalization of the maps from the toroidal compactifications of Siegel spaces to the Satake compactifications. We also show continuity of these maps for the case for the Hodge structure of Calabi-Yau threefolds with $h^{2,1} = 1$.