Boundaries of cycle spaces and degenerating Hodge structures

TL;DR

This paper investigates the properties of cycle spaces related to degenerating Hodge structures, constructing generalized maps from partial compactifications of period domains to Satake compactifications, with continuity shown for specific Calabi-Yau threefolds.

Contribution

It introduces new maps linking partial compactifications of period domains to Satake compactifications, extending previous constructions and analyzing their continuity in special cases.

Findings

Constructed generalized maps from period domain compactifications to Satake compactifications.

Proved continuity of these maps for Calabi-Yau threefolds with h^{2,1}=1.

Extended understanding of cycle spaces in degenerating Hodge structures.

Abstract

We study a property of cycle spaces in connection with degenerating Hodge structures of odd-weight, and 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 the continuity of these maps for the case of Calabi-Yau threefolds with h^{2,1}=1.