# Extension of Period Maps by Polyhedral Fans

@inproceedings{Deng2021ExtensionOP, title={Extension of Period Maps by Polyhedral Fans}, author={Haohua Deng}, year={2021} }

Kato and Usui developed a theory of partial compactifications for quotients of period domains D by arithmetic groups Γ, in an attempt to generalize the toroidal compactifications of AshMumford-Rapoport-Tai to non-classical cases. Their partial compactifications, which aim to fully compactify the images of period maps, rely on a choice of fan which is strongly compatible with Γ. In particular, they conjectured the existence of a complete fan, which would serve to simultaneously compactify all…

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