Tata Lectures on Theta II

• Κύριος συγγραφέας: Mumford, David (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2007.
• Σειρά: Modern Birkhäuser Classics
• Θέματα: Mathematics.; Algebraic geometry.; Functions of complex variables.; Partial differential equations.; Special functions.; Algebraic topology.; Physics.; Special Functions.; Algebraic Geometry.; Mathematical Methods in Physics.; Functions of a Complex Variable.; Algebraic Topology.; Partial Differential Equations.

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...

Πίνακας περιεχομένων:

• 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.