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Item Details
| Title:
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INTEGRABLE SYSTEMS IN THE REALM OF ALGEBRAIC GEOMETRY
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| By: |
Pol Vanhaecke |
| Format: |
Paperback |
| List price:
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£40.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
3540423370 |
| ISBN 13: |
9783540423379 |
| Publisher: |
SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG |
| Pub. date: |
31 July, 2001 |
| Edition: |
2nd ed. 2001 |
| Series: |
Lecture Notes in Mathematics v.1638 |
| Pages: |
264 |
| Description: |
Describes the general theory of Poisson structures and integrable systems on affine varieties, drawing special attention to algebraic completely integrable systems. This book also constructs and studies, in detail, several integrable systems, working out a few applications of integrable systems to algebraic geometry. |
| 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. |
| Illustrations: |
biography |
| Publication: |
Germany |
| Imprint: |
Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Returns: |
Returnable |
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Ramadan and Eid al-Fitr
A celebratory, inclusive and educational exploration of Ramadan and Eid al-Fitr for both children that celebrate and children who want to understand and appreciate their peers who do.
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