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Tata lectures on theta : II
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 differen...
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| Auteur principal : | |
|---|---|
| Autres auteurs : | , , |
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Tata lectures on theta. II / David Mumford; with the collaboration of C. Musili, M. Nori, E. Previato... [et al.] |
| Édition : | 1st ed. 2007. |
| Publié : |
Boston, MA :
Birkhäuser Boston
, [20..] Cham : Springer Nature |
| Collection : | Modern Birkhäuser classics (Internet) |
| Accès en ligne : |
Accès Nantes Université
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| Note sur l'URL : | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex |
| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | 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. |
| Sujets : | |
| Documents associés : | Autre format:
Tata lectures on theta Autre format: Tata lectures on theta Autre format: Tata Lectures on Theta II |
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| 200 | 1 | |a Tata lectures on theta |h II |f David Mumford |g with the collaboration of C. Musili, M. Nori, E. Previato... [et al.] | |
| 205 | |a 1st ed. 2007. | ||
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| 225 | 0 | |a Modern Birkhäuser Classics |x 2197-1811 | |
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| 327 | 1 | |a An Elementary Construction of Hyperelliptic Jacobians |a Review of background in algebraic geometry |a Divisors on hyperelliptic curves |a Algebraic construction of the Jacobian of a hyperelliptic curve |a The translation-invariant vector fields |a Neumann's dynamical system |a Tying together the analytic Jacobian and algebraic Jacobian |a Theta characteristics and the fundamental Vanishing Property |a Frobenius' theta formula |a Thomae's formula and moduli of hyperelliptic curves |a Characterization of hyperelliptic period matrices |a The hyperelliptic p-function |a The Korteweg-deVries dynamical system |a Fay's Trisecant Identity for Jacobian theta functions |a The Prime Form E(x,y). |a Fay's Trisecant Identity |a Corollaries of the identity |a Applications to solutions of differential equations |a The Generalized Jacobian of a Singular Curve and its Theta Function |a Resolution of algebraic equations by theta constants |a Resolution of algebraic equations by theta constants. | |
| 330 | |a 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 | ||
| 359 | 2 | |b An Elementary Construction of Hyperelliptic Jacobians |b Review of background in algebraic geometry |b Divisors on hyperelliptic curves |b Algebraic construction of the Jacobian of a hyperelliptic curve |b The translation-invariant vector fields |b Neumann s dynamical system |b Tying together the analytic Jacobian and algebraic Jacobian |b Theta characteristics and the fundamental Vanishing Property |b Frobenius theta formula |b Thomae s formula and moduli of hyperelliptic curves |b Characterization of hyperelliptic period matrices |b The hyperelliptic p-function |b The Korteweg-deVries dynamical system |b Fay s Trisecant Identity for Jacobian theta functions |b The Prime Form E(x,y). |b Fay s Trisecant Identity |b Corollaries of the identity |b Applications to solutions of differential equations |b The Generalized Jacobian of a Singular Curve and its Theta Function |b Resolution of algebraic equations by theta constants |b Resolution of algebraic equations by theta constants | |
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| 452 | | | |0 128506792 |t Tata lectures on theta |h II |f David Mumford |e Reprint of the 1984 edition |c Boston |n Birkhäuser |d 2007 |p 1 vol. (XIV-272 p.) |s Modern Birkhäuser classics |y 978-0-8176-4569-4 | |
| 452 | | | |0 128506792 |t Tata lectures on theta |h II |f David Mumford |e Reprint of the 1984 edition |c Boston |n Birkhäuser |d 2007 |p 1 vol. (XIV-272 p.) |s Modern Birkhäuser classics |y 978-0-8176-4569-4 | |
| 452 | | | |t Tata Lectures on Theta II |b Texte imprimé |y 9780817631109 | |
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