The new edition of this celebrated and long-unavailable book
preserves much of the content and structure of the original, which
is still unrivaled in its presentation of a universal method for
the resolution of a class of singularities in algebraic geometry.
At the same time, the book has been completely retypeset, errors
have been eliminated, proofs have been streamlined, the notation
has been made consistent and uniform, an index has been added, and
a guide to recent literature has been added. The authors begin by
reviewing key results in the theory of toroidal embeddings and by
explaining examples that illustrate the theory. Chapter II develops
the theory of open self-adjoint homogeneous cones and their
polyhedral reduction theory. Chapter III is devoted to basic facts
on hermitian symmetric domains and culminates in the construction
of toroidal compactifications of their quotients by an arithmetic
group. The final chapter considers several applications of the
general results. The book brings together ideas from algebraic
geometry, differential geometry, representation theory and number
theory, and will continue to prove of value for researchers and
graduate students in these areas.
General
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