Families of Varieties of General Type

János Kollár

2023년 4월 · Cambridge Tracts in Mathematics 231권 · Cambridge University Press

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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 A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.

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János Kollár is Professor of Mathematics at Princeton University. He has received the Cole Prize (2006), the Nemmers Prize (2016), and the Shaw Prize (2017). He is the author of more than 200 articles and ten books, mostly on algebraic geometry.