Tata Lectures on Theta II
By: Mumford, David [author.].
Contributor(s): SpringerLink (Online service).
Material type:
BookSeries: Modern Birkhäuser Classics: Publisher: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2007.Description: XIV, 272 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9780817645786.Subject(s): Mathematics | Algebraic geometry | Functions of complex variables | Partial differential equations | Special functions | Algebraic topology | Physics | Mathematics | Special Functions | Algebraic Geometry | Mathematical Methods in Physics | Functions of a Complex Variable | Algebraic Topology | Partial Differential EquationsDDC classification: 515.5 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
|
PK Kelkar Library, IIT Kanpur | Available | EBK9243 |
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.
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.
There are no comments for this item.