Families of Varieties of General Type

ISBN-13: 9781009346108 / Twarda / 2023 / 466 str.

New Jersey) Kollar Janos (Princeton University

Opis

The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.

Recenzje

'This excellent book provides a wealth of examples and technical details for those studying birational geometry and moduli spaces. It completely addresses several state-of-the-art topics in the field, including different stability notions, K-flatness, and subtleties in defining families of stable pairs over an arbitrary base. It will be an essential resource for both those first learning the subject and experts as it moves through history and examples before settling many of the (previously unknown) technicalities needed to define the correct moduli functor.' Kristin DeVleming, University of Massachusetts Amherst

Spis treści

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.