The research aims to construct a fine moduli space for log abelian varieties specifically with PEL structure.
Construction of the fine moduli space
Development of toroidal compactification
Analysis within the framework of abelian varieties
Successfully created a new moduli space for log abelian varieties
Established a connection to existing structures in the theory of abelian varieties
Abstract
We construct the fine moduli space of log abelian varieties with PEL structure, which gives a toroidal compactification of the moduli space of abelian varieties with PEL structure.