Toroidal Compactification of Siegel Spaces

Inhaltsverzeichnis

• The siegel upperhalf plane and the symplectic group.
• Main problem and main results.
• The case of g=1.
• Boundary components and the structure of parabolic subgroups.
• Realization as a siegel domain of the third kind, and satake compactification.
• Theory of torus embeddings.
• Toroidal compactification due to Mumford.
• Examples : reduction theory of positive quadratic forms.
• An application of the Voronoi compactification to the theory of moduli of polarized abelian varieties.