Families of varieties of general type
Author(s)
Bibliographic Information
Families of varieties of general type
(Cambridge tracts in mathematics, 231)
Cambridge University Press, 2023
- : hardback
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackKOL||14||8200043737793
Note
Includes bibliographical references (p. 446-461) and index
Description and Table of Contents
Description
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 A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.
Table of Contents
- Introduction
- Notation
- 1. History of moduli problems
- 2. One-parameter families
- 3. Families of stable varieties
- 4. Stable pairs over reduced base schemes
- 5. Numerical flatness and stability criteria
- 6. Moduli problems with flat divisorial part
- 7. Cayley flatness
- 8. Moduli of stable pairs
- 9. Hulls and husks
- 10. Ancillary results
- 11. Minimal models and their singularities
- References
- Index.
by "Nielsen BookData"