Families of varieties of general type

Author(s)

• Kollár, János
• Altmann, Klaus
• Kovács, Sándor J. (Sándor József)

Bibliographic Information

Families of varieties of general type

János Kollár ; with the collaboration of Klaus Altmann and Sándor J. Kovács

（Cambridge tracts in mathematics, 231）

Cambridge University Press, 2023

• : hardback

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 A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness, and Chapter 9 on hulls and husks.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

Details

• NCID: BD01735926
• ISBN:
  • 9781009346108
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge
• Pages/Volumes: xviii, 471 p.
• Size: 24 cm
• Classification:
  • DC23 : 516.35
• Subject Headings:
  • LCSH : Moduli theory
  • LCSH : Algebraic varieties
• Parent Bibliography ID:
  • BA00134372