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: Tata Lectures on Theta II
  name:
    name part: Mumford, David.
    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: 2007
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIV, 272 p. online resource.
  abstract: The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics. This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others. A definitive body of information and research on the subject of theta functions, this volume will be a useful addition to individual and mathematics research libraries.
  table of contents: An Elementary Construction of Hyperelliptic Jacobians -- Review of background in algebraic geometry -- Divisors on hyperelliptic curves -- Algebraic construction of the Jacobian of a hyperelliptic curve -- The translation-invariant vector fields -- Neumann’s dynamical system -- Tying together the analytic Jacobian and algebraic Jacobian -- Theta characteristics and the fundamental Vanishing Property -- Frobenius’ theta formula -- Thomae’s formula and moduli of hyperelliptic curves -- Characterization of hyperelliptic period matrices -- The hyperelliptic p-function -- The Korteweg-deVries dynamical system -- Fay’s Trisecant Identity for Jacobian theta functions -- The Prime Form E(x,y). -- Fay’s Trisecant Identity -- Corollaries of the identity -- Applications to solutions of differential equations -- The Generalized Jacobian of a Singular Curve and its Theta Function -- Resolution of algebraic equations by theta constants -- Resolution of algebraic equations by theta constants.
  note: by David Mumford.
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic geometry
  subject:
    topic: Functions of complex variables
  subject:
    topic: Partial differential equations
  subject:
    topic: Special functions
  subject:
    topic: Algebraic topology
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Special Functions
  subject:
    topic: Algebraic Geometry
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Functions of a Complex Variable
  subject:
    topic: Algebraic Topology
  subject:
    topic: Partial Differential Equations
  classification: QA351
  classification: 515.5
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Modern Birkhäuser Classics
  identifier: 9780817645786
  identifier: http://dx.doi.org/10.1007/978-0-8176-4578-6
  record info:
    record creation date: 120414
    record change date: 20151218142517.0
    record identifier: 978-0-8176-4578-6