Families of varieties of general type
著者
書誌事項
Families of varieties of general type
（Cambridge tracts in mathematics, 231）
Cambridge University Press, 2023
- : hardback
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注記
Includes bibliographical references (p. 446-461) and index
内容説明・目次
内容説明
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 A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.
目次
- 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.
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