Download EBOOK Integrable Systems in the Realm of Algebraic Geometry PDF for free
 
Category: Science & Geography
The author of the book: Pol Vanhaecke
Format files: PDF, EPUB, TXT, DOCX
The size of the: 35.84 MB
Language: English
ISBN13: 9783540423379
Edition: SpringerVerlag Berlin and Heidelberg GmbH & Co. K
Date of issue: 1 August 2001

Description of the book "Integrable Systems in the Realm of Algebraic Geometry":
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 RiemannRoch 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 nongeneric 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 twodkmensional a.e.i, systems ...138. 5. Lax equations ...140. VI. The PDF Mumford systems ...143. 1. Introduction ...143. 2. Genesis ...145. 2.1. The algebra of pseudodifferential 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. MultiHamiltonian structure and symmetries ...155. 3.1. The loop algebra 9(q ...155. 3.2. Reducing the Rbrackets 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.
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Pol Vanhaecke
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