rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Families of varieties of general type
  name:
    name part: Kollár, János
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Altmann, Klaus
    name part: (Mathematician)
    role:
      role term: contributor.
  name:
    name part: Kovács, Sándor J. (Sándor József)
    role:
      role term: contributor.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: enk
    date issued: 2023
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xviii, 471 pages ; 24 cm.
  abstract: 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 A wealth of previously unpublished material is also featured, including Chapter 5 on numerical flatness criteria, Chapter 7 on K-flatness and Chapter 9 on hulls and husks.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: History of moduli problems -- One-parameter families -- Families of stable varieties -- Stable pairs over reduced base schemes -- Numerical flatness and stability criteria -- Moduli problems with flat divisorial part -- Cayley flatness -- Moduli of stable pairs -- Hulls and husks -- Ancillary results -- Minimal models and their singularities.
  note: János Kollár, Princeton University, New Jersey with the collaboration of Klaus Altmann, Freie Universitat Berlin, and Sándor J. Kovács, University of Washington.
  note: Includes bibliographical references (pages 446-471) and index.
  subject:
    topic: Algebraic varieties
  subject:
    topic: Moduli theory
  classification: 516.35
  related item:
    title info:
      title: Cambridge tracts in mathematics ; 231
  identifier: 9781009346108
  identifier: 1009346105
  identifier: 9781009346115
  identifier: 9781009346146
  record info:
    record content source: KEI
    record creation date: 230604
    record change date: 20251002130551.3
    record identifier: in00005663920