Kato-Usui partial compactifications over the toroidal compactifications of Siegel spaces

摘要

We construct fans which give Kato-Usui partial compactifications of period domains of weight — 1. Similarly to the fans of toroidal compactifications, these fans are given by polyhedral decompositions. We also demonstrate a fibration structure for some kinds of Kato-Usui boundary components.