Families Of Varieties Of General Type

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 A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks. Gradually builds from the simplest theories to the most general one, allowing readers to see the development of the ideas and reach important special cases quickly Provides many worked-out examples, demonstrating the natural limits of all concepts and theorems Includes a wealth of previously unpublished material, providing a basis and solid references for future work