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: Deformation Theory
  name:
    name part: Hartshorne, Robin.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2010
    edition: 1.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VIII, 234 p. 19 illus. online resource.
  abstract: The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. Topics include: * deformations over the dual numbers; * smoothness and the infinitesimal lifting property; * Zariski tangent space and obstructions to deformation problems; * pro-representable functors of Schlessinger; * infinitesimal study of moduli spaces such as the Hilbert scheme, Picard scheme, moduli of curves, and moduli of stable vector bundles. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.
  table of contents: First-Order Deformations -- Higher-Order Deformations -- Formal Moduli -- Global Questions.
  note: by Robin Hartshorne.
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic geometry
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic Geometry
  classification: QA564-609
  classification: 516.35
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Graduate Texts in Mathematics, 257
  identifier: 9781441915962
  identifier: http://dx.doi.org/10.1007/978-1-4419-1596-2
  record info:
    record creation date: 100301
    record change date: 20151204153444.0
    record identifier: 978-1-4419-1596-2