Families of Varieties of General Type

This book gives the first complete treatment of the moduli theory of varieties of dimension larger than one, aimed at researchers and graduate students in algebraic geometry and related areas. The first chapter provides a historical introduction to the subject, while later chapters provide all necessary background material.

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This book establishes the moduli theory of stable varieties, giving the optimal approach to understanding families of varieties of general type. Starting from the Deligne–Mumford theory of the moduli of curves and using Mori's program as a main tool, the book develops the techniques necessary for a theory in all dimensions. The main results give all the expected general properties, including a projective coarse moduli space. A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.