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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| Další autoři: | , , |
| Médium: | Livre numérique |
| Jazyk: | Anglais |
| Vydáno: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Vydání: | 1st ed. 2007. |
| Edice: | Modern Birkhäuser Classics
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| Témata: | |
| On-line přístup: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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Contributeurs : Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Tata lectures on theta, II, David Mumford, Reprint of the 1984 edition, Boston, Birkhäuser, 2007, 1 vol. (XIV-272 p.), Modern Birkhäuser classics, 978-0-8176-4569-4 • Tata lectures on theta, II, David Mumford, Reprint of the 1984 edition, Boston, Birkhäuser, 2007, 1 vol. (XIV-272 p.), Modern Birkhäuser classics, 978-0-8176-4569-4 • Tata Lectures on Theta II, Texte imprimé, 9780817631109 |
Obsah:
- 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.
- 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