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The classification theory of algebraic varieties is the focus of
this book. This very active area of research is still developing,
but an amazing quantity of knowledge has accumulated over the past
twenty years. The authors goal is to provide an easily accessible
introduction to the subject. The book starts with preparatory and
standard definitions and results, then moves on to discuss various
aspects of the geometry of smooth projective varieties with many
rational curves, and finishes in taking the first steps towards
Moris minimal model program of classification of algebraic
varieties by proving the cone and contraction theorems. The book is
well-organized and the author has kept the number of concepts that
are used but not proved to a minimum to provide a mostly
self-contained introduction.
Higher-dimensional algebraic geometry studies the classification theory of algebraic varieties. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The author¿s goal is to provide an easily accessible introduction to the subject. The book covers preparatory and standard definitions and results, moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Mori¿s minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction to graduate students and researchers.
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