A new and complete treatment of semi-abelian degenerations of
abelian varieties, and their application to the construction of
arithmetic compactifications of Siegel moduli space, with most of
the results being published for the first time. Highlights of the
book include a classification of semi-abelian schemes, construction
of the toroidal and the minimal compactification over the integers,
heights for abelian varieties over number fields, and Eichler
integrals in several variables, together with a new approach to
Siegel modular forms. A valuable source of reference for
researchers and graduate students interested in algebraic geometry,
Shimura varieties or diophantine geometry.
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