Integrable systems in the realm of algebraic geometry
Author(s)
Bibliographic Information
Integrable systems in the realm of algebraic geometry
(Lecture notes in mathematics, 1638)
Springer, c2001
2nd ed
Available at 42 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
Bibliography: p. 243-251
Includes index
Description and Table of Contents
Description
2. Divisors and line bundles ...99. 2.1. Divisors ...99. 2.2. Line bundles ...100. 2.3. Sections of line bundles ...101. 2.4. The Riemann-Roch Theorem ...103. 2.5. Line bundles and embeddings in projective space ...105. 2.6. Hyperelliptic curves ...106. 3. Abelian varieties ...108. 3.1. Complex tori and Abelian varieties ...108. 3.2. Line bundles on Abelian varieties ...109. 3.3. Abelian surfaces ...111. 4. Jacobi varieties ...114. 4.1. The algebraic Jacobian ...114. 4.2. The analytic/transcendental Jacobian ...114. 4.3. Abel's Theorem and Jacobi inversion ...119. 4.4. Jacobi and Kummer surfaces ...121. 5. Abelian surfaces of type (1,4) ...123. 5.1. The generic case ...123. 5.2. The non-generic case ...124. V. Algebraic completely integrable Hamiltonian systems ...127. 1. Introduction ...127. 2. A.c.i. systems ...129. 3. Painlev~ analysis for a.c.i, systems ...135. 4. The linearization of two-dkmensional a.e.i, systems ...138. 5. Lax equations ...140. VI. The Mumford systems ...143. 1. Introduction ...143. 2. Genesis ...145. 2.1. The algebra of pseudo-differential operators ...145. 2.2. The matrix associated to two commuting operators ...146. 2.3. The inverse construction ...150.
2.4. The KP vector fields ...152. ix 3. Multi-Hamiltonian structure and symmetries ...155. 3.1. The loop algebra 9(q ...155. 3.2. Reducing the R-brackets and the vector field ~ ...157. 4. The odd and the even Mumford systems ...161. 4.1. The (odd) Mumford system ...161. 4.2. The even Mumford system ...163.
Table of Contents
I. Introduction: II. Integrable Hamiltonian systems on affine Poisson varieties: 1. Introduction.- 2. Affine Poisson varieties and their morphisms.- 3. Integrable Hamiltonian systems and their morphisms.- 4. Integrable Hamiltonian systems on other spaces.- III. Integrable Hamiltonian systems and symmetric products of curves: 1. Introduction.- 2. The systems and their integrability.- 3. The geometry of the level manifolds.- IV. Interludium: the geometry of Abelian varieties 1. Introduction.- 2. Divisors and line bundles.- 3. Abelian varieties.- 4. Jacobi varieties.- 5. Abelian surfaces of type (1,4).- V. Algebraic completely integrable Hamiltonian systems: 1. Introduction.- 2. A.c.i. systems.- 3. Painlev analysis for a.c.i. systems.- 4. The linearization of two-dimensional a.c.i. systems.- 5. Lax equations.- VI. The Mumford systems 1. Introduction.- 2. Genesis.- 3. Multi-Hamiltonian structure and symmetries.- 4. The odd and the even Mumford systems.- 5. The general case.- VII. Two-dimensional a.c.i. systems and applications 1. Introduction.- 2. The genus two Mumford systems.- 3. Application: generalized Kummersurfaces.- 4. The Garnier potential.- 5. An integrable geodesic flow on SO(4).- 6. The Hnon-Heiles hierarchy.- 7. The Toda lattice.- References.- Index.
by "Nielsen BookData"