Kato-Usui partial compactifications over the toroidal compactifications of Siegel spaces
Tatsuki Hayama
TL;DR
This paper constructs specific fans for Kato-Usui partial compactifications of Siegel space period domains, revealing a polyhedral structure and a fibration in certain boundary components, advancing understanding of their geometric structure.
Contribution
It introduces new fans for Kato-Usui compactifications of Siegel spaces and demonstrates a fibration structure in some boundary components.
Findings
Fans are given by polyhedral decompositions similar to toroidal compactifications.
Constructed fans enable Kato-Usui partial compactifications of weight -1 period domains.
Identified a fibration structure in certain boundary components.
Abstract
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 show a fibration structure for some kind of Kato-Usui boundary components.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometric and Algebraic Topology · Advanced Operator Algebra Research