Integrable systems in the realm of algebraic geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2001
|
| Edition: | 2. ed. |
| Series: | Lecture notes in mathematics
1638 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 243 - 251 |
| Physical Description: | X, 256 S. graph. Darst. |
| ISBN: | 3540423370 |
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| 245 | 1 | 0 | |a Integrable systems in the realm of algebraic geometry |c Pol Vanhaecke |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London |b Springer |c 2001 | |
| 300 | |a X, 256 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1638 | |
| 500 | |a Literaturverz. S. 243 - 251 | ||
| 650 | 4 | |a Systèmes hamiltoniens | |
| 650 | 4 | |a Variétés abéliennes | |
| 650 | 4 | |a Abelian varieties | |
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TABLE OF CONTENTS 1. INTRODUCTION . . . . . . . . . . . . . . . . . . .
. . . . . . . . 1. IT. INTEGRABLE HAMILTONIAN SYSTEMS ON AFFINE POISSON
VARIETIES . . . . . . 17. 1. INTRODUCTION . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . 17. 2. AFFINE POISSON VARIETIES AND THEIR
MORPHISMS . . . . . . . . . . . . . . . . 19. 2.1. AFFINE POISSON
VARIETIES . . . . . . . . . . . . . . . . . . . . . . . 19. 2.2.
MORPHISMS OF AFFINE POISSON VARIETIES . . . . . . . . . . . . . . . . .
26. 2.3. CONSTRUCTIONS OF AFFINE POISSON VARIETIES . . . . . . . . . . .
. . . . . 28. 2.4. DECOMPOSITIONS AND INVARIANTS OF AFFINE POISSON
VARIETIES . . . . . . . . . 37. 3. INTEGRABLE HAMILTONIAN SYSTEMS AND
THEIR MORPHISMS . . . . . . . . . . . . 47. 3.1. INTEGRABLE HAMILTONIAN
SYSTEMS ON AFFINE POISSON VARIETIES . . . . . . . . 47. 3.2. MORPHISMS
OF INTEGRABLE HAMILTONIAN SYSTEMS . . . . . . . . . . . . . 54. 3.3.
CONSTRUCTIONS OF INTEGRABLE HAMILTONIAN SYSTEMS . . . . . . . . . . . .
57. 3.4. COMPATIBLE AND MULTI-HAMILTONIAN INTEGRABLE SYSTEMS . . . . . .
. . . . 62. 4. INTEGRABLE HAMILTONIAN SYSTEMS ON OTHER SPACES . . . . .
. . . . . . . . . . 65. 4.1. POISSON SPACES . . . . . . . . . . . . . .
. . . . . . . . . . . . . 65. 4.2. INTEGRABLE HAMILTONIAN SYSTEMS ON
POISSON SPACES . . . . . . . . . . . . 69. 111. INTEGRABLE HAMILTONIAN
SYSTEMS AND SYMMETRIC PRODUCTS OF CURVES . 71. 1. INTRODUCTION . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 71. 2. THE SYSTEMS AND
THEIR INTEGRABILITY . . . . . . . . . . . . . . . . . . . . 73. 2.1.
NOTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.
2.2. THE COMPATIBLE POISSON STRUCTURES -JW D 73. 2.3. POLYNOMIAJS IN
INVOLUTION FOR I., -1D' 78. 2.4. THE HYPERELLIPTIC CASE . . . . . . . .
. . . . . . . . . . . . . . . . 83. 3. THE GEOMETRY OF THE LEVEL
MANIFOLDS . . . . . . . . . . . . . . . . . . . . 85. 3.1. THE REAL AND
COMPLEX LEVEL SETS . . . . . . . . . . . . . . . . . . . . 85. 3.2. THE
STRUCTURE OF THE COMPLEX LEVEL MANIFOLDS . . . . . . . . . . . . . . 87.
3.3. THE STRUCTURE OF THE REAL LEVEL MANIFOLDS . . . . . . . . . . . . .
. . . 89. 3.4. COMPACTIFICATION OF THE COMPLEX LEVEL MANIFOLDS . . . . .
. . . . . . . 93. 3.5. THE SIGNIFICANCE OF THE POISSON STRUCTURES -J'P D
. . 95. VIII IV. INTERLUDIUM: THE GEOMETRY OF ABELIAN VARIETIES . . . .
. . . . . . 97. 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . 97. 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. PAINLEV6 ANALYSIS FOR A.C.I. SYSTEMS . . . . . . . . . . . . . . . .
. . . . 135. 4. THE LINEARIZATION OF TWO-DIMENSIONAL A.C.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. THEKP VECTOR FIELDS . . . . . . . . . . . . . . . . . . .
. . . . . 152. IX 3. MULTI-HAMILTONIAN STRUCTURE AND SYMMETRIES . . . .
. . . . . . . . . . . . 155. 3.1. THE LOOP ALGEBRA 91, . . . . . . . . .
. . . . . . . . . . . . . . . 155. 3.2. PTEDUCING THE R-BRACKETS AND THE
VECTOR FIELDV . . . . . . . . . . . . . 157. 4. THE ODD AND THE EVEN
MUMFORD SYSTEMS . . . . . . . . . . . . . . . . . . 161. 4.1. THE (ODD)
MUMFORD SYSTEM . . . . . . . . . . . . . . . . . . . . . 161. 4.2. THE
EVEN MUMFORD SYSTEM . . . . . . . . . . . . . . . . . . . . . . 163.
4.3. ALGEBRAIC COMPLETE INTEGRABILITY AND LAURENT SOLUTIONS . . . . . .
. . . . 164. 5. THE GENERAL CASE . . . . . . . . . . . . . . . . . . . .
. . . . . . . . 168. VII. TWO-DIMENSIONAL A.C.I. SYSTEMS AND
APPLICATIONS . . . . . . . . . 175. 1. INTRODUCTION . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . 175. 2. THE GENUS TWO MUMFORD.
SYSTEMS . . . . . . . . . . . . . . . . . . . . . 177. 2.1. THE GENUS
TWO ODD MUMFORD, SYSTEM . . . . . . . . . . . . . . . . . 177. 2.2. THE
GENUS TWO EVEN MUMFORD SYSTEM . . . . . . . . . . . . . . . . . 179.
2.3. THE BECHLIVANIDIS-VAN MOERBEKE SYSTEM . . . . . . . . . . . . . . .
. 181. 3. APPLICATION: GENERALIZED KUMMER SURFACES . . . . . . . . . . .
. . . . . . 185. 3.1. GENUS TWO CURVES WITH AN AUTOMORPHISM OF ORDER
THREE . . . . . . . . . 185. 3.2. THE 94 CONFIGURATION ON THE JACOBIAN
OFR . . . . . . . . . . . . . . . 186. 3.3. A PROJECTIVE EMBEDDING OF
THE GENERALISED KUMMER SURFACE . . . . . . . . 190. 4. THE GAXNIER
POTENTIAL . . . . . . . . . . . . . . . . . . . . . . . . . . 196. 4.1.
THE GARNIER POTENTIAL AND ITS INTEGRABILITY . . . . . . . . . . . . . .
. 196. 4.2. SOME MODULI SPACES OF ABELIAN SURFACES OF TYPE (1,4) . . . .
. . . . . . 202. 4.3. THE PRECISE RELATION WITH THE CANONICAL JACOBIAN .
. . . . . . . . . . . 206. 4.4. THE RELATION WITH THE CANONICAL JACOBIAN
MADE EXPLICIT . . . . . . . . . 211. 4.5. THE CENTRAL GARNIER POTENTIALS
. . . . . . . . . . . . . . . . . . . . 216. 5. AN INTEGRABLE GEODESIC
FLOW ON SO(4) . . . . . . . . . . . . . . . . . . . 220. 5.1. THE
GEODESIC FLOW ON SO(4) FOR METRIC II . . . . . . . . . . . . . . . .
220. 5.2. LINEARIZING VARIABLES . . . . . . . . . . . . . . . . . . . .
. . . . . 222. 5.3. THE MAPM -+M . . . . . . . . . . . . . . . . . . . .
. . . . . . 226. 6. THE H6NON-HEILES HIERARCHY . . . . . . . . . . . . .
. . . . . . . . . . 230. 6.1. THE CUBIC H6NON-HEILES POTENTIAL . . . . .
. . . . . . . . . . . . . . 230. 6.2. THE QUARTIC H6NON-HEILES POTENTIAL
. . . . . . . . . . . . . . . . . . 232. 6.3. THE H6NON-HEILES HIERARCHY
. . . . . . . . . . . . . . . . . . . . . 233. 7. THE TODA LATTICE . . .
. . . . . . . . . . . . . . . . . . . . . . . . . 235. 7.1. DIFFERENT
FORMS OF THE TODA LATTICE . . . . . . . . . . . . . . . . . . 235. 7.2.
A MORPHISM, TO THE GENUS 2 EVEN MUMFORD SYSTEM . . . . . . . . . . . .
237. 7.3. TODA AND ABELIAN SURFACES OF TYPE (1,3) . . . . . . . . . . .
. . . . . 240. REFERENCES . . . . . . . . . . . . . . . . . . . . . . .
. . . . . 243. INDEX . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . 253. X |
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| dewey-full | 516.3/53 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-20T07:38:59Z |
| institution | BVB |
| isbn | 3540423370 |
| language | English |
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| physical | X, 256 S. graph. Darst. |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Vanhaecke, Pol 1963- Verfasser (DE-588)1028305303 aut Integrable systems in the realm of algebraic geometry Pol Vanhaecke 2. ed. Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2001 X, 256 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1638 Literaturverz. S. 243 - 251 Systèmes hamiltoniens Variétés abéliennes Abelian varieties Hamiltonian systems Integrables System (DE-588)4114032-1 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Integrables System (DE-588)4114032-1 s Algebraische Geometrie (DE-588)4001161-6 s DE-604 Lecture notes in mathematics 1638 (DE-604)BV000676446 1638 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009454342&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vanhaecke, Pol 1963- Integrable systems in the realm of algebraic geometry Lecture notes in mathematics Systèmes hamiltoniens Variétés abéliennes Abelian varieties Hamiltonian systems Integrables System (DE-588)4114032-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4114032-1 (DE-588)4001161-6 |
| title | Integrable systems in the realm of algebraic geometry |
| title_auth | Integrable systems in the realm of algebraic geometry |
| title_exact_search | Integrable systems in the realm of algebraic geometry |
| title_full | Integrable systems in the realm of algebraic geometry Pol Vanhaecke |
| title_fullStr | Integrable systems in the realm of algebraic geometry Pol Vanhaecke |
| title_full_unstemmed | Integrable systems in the realm of algebraic geometry Pol Vanhaecke |
| title_short | Integrable systems in the realm of algebraic geometry |
| title_sort | integrable systems in the realm of algebraic geometry |
| topic | Systèmes hamiltoniens Variétés abéliennes Abelian varieties Hamiltonian systems Integrables System (DE-588)4114032-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Systèmes hamiltoniens Variétés abéliennes Abelian varieties Hamiltonian systems Integrables System Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009454342&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT vanhaeckepol integrablesystemsintherealmofalgebraicgeometry |