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: Algebraic Surfaces and Holomorphic Vector Bundles
  name:
    name part: Friedman, Robert.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 1998
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (ix, 329 pages)
  abstract: This book covers the theory of algebraic surfaces and holomorphic vector bundles in an integrated manner. It is aimed at graduate students who have had a thorough first year course in algebraic geometry (at the level of Hartshorne's ALGEBRAIC GEOMETRY), as well as more advanced graduate students and researchers in the areas of algebraic geometry, gauge thoery, or 4-manifold topolgogy. Many of the results on vector bundles should also be of interest to physicists studying string theory. A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, and are studied in alternate chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, and then the geometry of vector bundles over such surfaces is analyzed. Many of the results on vector bundles appear for the first time in book form, suitable for graduate students. The book also has a strong emphasis on examples, both of surfaces and vector bundles. There are over 100 exercises which form an integral part of the text.
  table of contents: Curves on a Surface -- Coherent Sheaves -- Birational Geometry -- Stability -- Some examples of surfaces -- Vector Bundles over Ruled Surfaces -- An Introduction to Elliptic Surfaces -- Vector Bundles over Elliptic Surfaces -- Bogomolov's Inequality and Applications -- Classification of Algebraic Surfaces and of Stable Bundles.
  note: by Robert Friedman.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Mathematics
  classification: QA564-609
  classification: 516.35
  related item:
    title info:
      title: Universitext
  identifier: 9781461216889 (electronic bk.)
  identifier: 1461216885 (electronic bk.)
  identifier: 9781461272465
  identifier: 1461272467
  identifier: 1461216885
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 121227
    record change date: 20260420201316.7
    record identifier: in00003561843
    language of cataloging:
      language term: eng