Tata Lectures on Theta II / by David Mumford
(Modern Birkhäuser Classics)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser |
| 出版年 | 2007 |
| 本文言語 | 英語 |
| 大きさ | XIV, 272 p : online resource |
書誌詳細を非表示
| 内容注記 | 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 |
|---|---|
| 一般注記 | 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 |
| 著者標目 | *Mumford, David author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebraic geometry LCSH:Functions of complex variables LCSH:Partial differential equations LCSH:Special functions LCSH:Algebraic topology LCSH:Physics FREE:Mathematics FREE:Special Functions FREE:Algebraic Geometry FREE:Mathematical Methods in Physics FREE:Functions of a Complex Variable FREE:Algebraic Topology FREE:Partial Differential Equations |
| 分 類 | DC23:515.5 |
| 巻冊次 | ISBN:9780817645786 
|
| ISBN | 9780817645786 |
| URL | http://dx.doi.org/10.1007/978-0-8176-4578-6 |
目次／あらすじ