Mumford, David
Tata Lectures on Theta II
IIIa:. An Elementary Construction of Hyperelliptic Jacobians
1. Review of background in algebraic geometry
David Mumford
2. Divisors on hyperelliptic curves
David Mumford
3. Algebraic construction of the Jacobian of a hyperelliptic curve
David Mumford
4. The translation-invariant vector fields
David Mumford
5. Neumann’s dynamical system
David Mumford
6. Tying together the analytic Jacobian and algebraic Jacobian
David Mumford
7. Theta characteristics and the fundamental Vanishing Property
David Mumford
8. Frobenius’ theta formula
David Mumford
9. Thomae’s formula and moduli of hyperelliptic curves
David Mumford
10. Characterization of hyperelliptic period matrices
David Mumford
11. The hyperelliptic p-function
David Mumford
12. The Korteweg-deVries dynamical system
David Mumford
IIIb:. Fay’s Trisecant Identity for Jacobian theta functions
13. The Prime Form E(x,y).
David Mumford
14. Fay’s Trisecant Identity
David Mumford
15. Corollaries of the identity
David Mumford
16. Applications to solutions of differential equations
David Mumford
17. The Generalized Jacobian of a Singular Curve and its Theta Function
David Mumford
18. Resolution of algebraic equations by theta constants
Hiroshi Umemura
Avainsanat: Mathematics, Special Functions, Algebraic Geometry, Mathematical Methods in Physics, Functions of a Complex Variable, Algebraic Topology, Partial Differential Equations
- Tekijä(t)
- Mumford, David
- Julkaisija
- Springer
- Julkaisuvuosi
- 2007
- Kieli
- en
- Painos
- 1
- Sarja
- Modern Birkhäuser Classics
- Sivumäärä
- 286 sivua
- Kategoria
- Eksaktit luonnontieteet
- Tiedostomuoto
- E-kirja
- eISBN (PDF)
- 9780817645786