Integrable Systems in the Realm of Algebraic Geometry - Couverture souple

Vanhaecke, Pol

Couverture souple

ISBN 10 : 3540423370 ISBN 13 : 9783540423379

Editeur : Springer, 2008

Synopsis

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2008
• Langue: anglais
• ISBN 10: 3540423370
• ISBN 13: 9783540423379
• Reliure: Broché
• Numéro d'édition: 2
• Nombre de pages: 276
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne