Verfügbarkeit: Integrable systems in the realm of algebraic geometry

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Bibliographische Detailangaben
Beteilige Person:	Vanhaecke, Pol 1963- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2001
Ausgabe:	2. ed.
Schriftenreihe:	Lecture notes in mathematics 1638
Schlagwörter:	Systèmes hamiltoniens Variétés abéliennes Abelian varieties Hamiltonian systems Algebraische Geometrie Integrables System
Links:	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
Beschreibung:	Literaturverz. S. 243 - 251
Umfang:	X, 256 S. graph. Darst.
ISBN:	3540423370

Internformat

MARC


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Datensatz im Suchindex

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adam_text	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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illustrated	Illustrated
indexdate	2024-12-20T10:54:11Z
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isbn	3540423370
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-009454342
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publisher	Springer
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series	Lecture notes in mathematics
series2	Lecture notes in mathematics
spellingShingle	Vanhaecke, Pol 1963- Integrable systems in the realm of algebraic geometry Lecture notes in mathematics Systèmes hamiltoniens Variétés abéliennes Abelian varieties Hamiltonian systems Algebraische Geometrie (DE-588)4001161-6 gnd Integrables System (DE-588)4114032-1 gnd
subject_GND	(DE-588)4001161-6 (DE-588)4114032-1
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 Algebraische Geometrie (DE-588)4001161-6 gnd Integrables System (DE-588)4114032-1 gnd
topic_facet	Systèmes hamiltoniens Variétés abéliennes Abelian varieties Hamiltonian systems Algebraische Geometrie Integrables System
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volume_link	(DE-604)BV000676446
work_keys_str_mv	AT vanhaeckepol integrablesystemsintherealmofalgebraicgeometry

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