Families of Varieties of General Type
Seiten
2023
Cambridge University Press (Verlag)
978-1-009-34610-8 (ISBN)
Cambridge University Press (Verlag)
978-1-009-34610-8 (ISBN)
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.
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 A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.
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 A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.
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.
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.
| Erscheinungsdatum | 03.04.2023 |
|---|---|
| Reihe/Serie | Cambridge Tracts in Mathematics |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 159 x 235 mm |
| Gewicht | 880 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-009-34610-5 / 1009346105 |
| ISBN-13 | 978-1-009-34610-8 / 9781009346108 |
| Zustand | Neuware |
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