Applied Picard-Lefschetz theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2002
|
| Schriftenreihe: | Mathematical surveys and monographs
97 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 313-320) and index |
| Beschreibung: | XI, 324 S. Ill. |
| ISBN: | 0821829483 |
Internformat
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| 490 | 1 | |a Mathematical surveys and monographs |v 97 | |
| 500 | |a Includes bibliographical references (p. 313-320) and index | ||
| 650 | 7 | |a EQUAÇÕES DIFERENCIAIS PARCIAIS HIPERBÓLICAS |2 larpcal | |
| 650 | 7 | |a FUNÇÕES DE VÁRIAS VARIÁVEIS COMPLEXAS |2 larpcal | |
| 650 | 7 | |a GEOMETRIA ALGÉBRICA |2 larpcal | |
| 650 | 7 | |a GRUPOS DE MONODROMIA |2 larpcal | |
| 650 | 7 | |a SINGULARIDADES (GEOMETRIA ALGÉBRICA) |2 larpcal | |
| 650 | 7 | |a TEORIA DE PICARD-LEFSCHETZ |2 larpcal | |
| 650 | 4 | |a Integral representations | |
| 650 | 4 | |a Picard-Lefschetz theory | |
| 650 | 4 | |a Singularities (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804132797880729600 |
|---|---|
| adam_text | MATHEMATICAL SURVEYS AND MONOGRAPHS VOLUME 97 APPLIED PICARD-LEFSCHETZ
THEORY V. A. VASSILIEV AMERICAN MATHEMATICAL SOCIETY CONTENTS PREFACE IX
INTRODUCTION 1 1. MONODROMY AND ITS LOCALIZATION 1 2. NEWTON S PROBLEM
ON THE INTEGRABILITY OF OVALS 6 3. SURFACE POTENTIALS 13 4. PETROVSKII
THEORY OF LACUNAS FOR HYPERBOLIC OPERATORS 18 5. HYPERGEOMETRIC
INTEGRALS 22 CHAPTER I. LOCAL MONODROMY THEORY OF ISOLATED SINGULARITIES
OF FUNCTIONS AND COMPLETE INTERSECTIONS 29 1. GAUFI-MANIN CONNECTION IN
HOMOLOGICAL BUNDLES. MONODROMY AND VARIATION OPERATORS 29 2.
PICARD-LEFSCHETZ FORMULA 32 3. MONODROMY THEORY OF ISOLATED FUNCTION
SINGULARITIES 37 4. DYNKIN DIAGRAMS OF REAL SINGULARITIES OF FUNCTIONS
OF TWO VARIABLES (AFTER S.M. GUSEIN-ZADE AND N. A CAMPO) 51 5.
CLASSIFICATION OF SINGULARITIES OF SMOOTH FUNCTIONS 56 6.
LYASHKO-LOOIJENGA COVERING 62 7. COMPLEMENTS OF DISCRIMINANTS OF REAL
SIMPLE SINGULARITIES (AFTER E. LOOIJENGA) 65 8. PHAM SINGULARITIES 67 9.
SINGULARITIES AND LOCAL MONODROMY OF COMPLETE INTERSECTIONS 71 CHAPTER
II. STRATIFIED PICARD-LEFSCHETZ THEORY AND MONODROMY OF HYPERPLANE
SECTIONS 75 1. STRATIFICATIONS OF SEMIANALYTIC AND SUBANALYTIC SETS 76
2. MONODROMY OF HYPERPLANE SECTIONS 79 3. SIMPLEST FACTS ON INTERSECTION
HOMOLOGY THEORY 89 4. STRATIFIED PICARD-LEFSCHETZ THEORY 91 CHAPTER III.
NEWTON S THEOREM ON THE NON-INTEGRABILITY OF OVALS 111 1. INTRODUCTION
111 2. REDUCTION TO MONODROMY THEORY 117 3. THE CLASS CAP 119 4.
RAMIFICATION OF INTEGRATION CHAINS AT NON-SINGULAR POINTS 121 5.
EXAMPLES 124 VI CONTENTS 6. OBSTRUCTIONS TO INTEGRABILITY ARISING FROM
CUSPIDAL EDGES. PROOF OF THEOREM 1.8 126 7. RAMIFICATION CLOSE TO
ASYMPTOTIC HYPERPLANES. PROOF OF THEOREM 1.9 133 8. OPEN PROBLEMS 136
CHAPTER IV. LACUNAS AND LOCAL PETROVSKII CONDITION FOR HYPERBOLIC
DIFFERENTIAL OPERATORS WITH CONSTANT COEFFICIENTS 137 1. INTRODUCTION
137 2. HYPERBOLIC POLYNOMIALS 140 3. HYPERBOLIC OPERATORS AND HYPERBOLIC
POLYNOMIALS. SHARPNESS, DIFFUSION, AND LACUNAS 142 4. GENERATING
FUNCTIONS AND GENERATING FAMILIES OF WAVE FRONTS. CLASSIFICATION OF
SINGULAR POINTS OF WAVE FRONTS 146 5. LOCAL LACUNAS CLOSE TO
NON-SINGULAR POINTS OF FRONTS AND CLOSE TO SINGULAR POINTS OF TYPES AI
AND ^3 (AFTER DAVYDOVA, BOROVIKOV AND GARDING) 149 6. PETROVSKII AND
LERAY CYCLES. HERGLOTZ-PETROVSKII-LERAY FORMULA. PETROVSKII CONDITION
FOR GLOBAL LACUNAS 151 7. LOCAL PETROVSKII CONDITION AND LOCAL
PETROVSKII CYCLE. LOCAL PETROVSKII CONDITION IMPLIES SHARPNESS 155 8.
SHARPNESS IMPLIES THE LOCAL PETROVSKII CONDITION CLOSE TO THE FINITE
TYPE POINTS OF WAVE FRONTS 159 9. LOCAL PETROVSKII CONDITION CAN BE
STRONGER THAN SHARPNESS 162 10. NORMAL FORMS OF NON-SHARPNESS AT THE
SINGULARITIES OF WAVE FRONTS (AFTER A.N. VARCHENKO) 162 11. PROBLEMS 164
CHAPTER V. CALCULATION OF LOCAL PETROVSKII CYCLES AND ENUMERATION OF
LOCAL LACUNAS CLOSE TO REAL SINGULARITIES 165 1. MAIN THEOREMS 165 2.
LOCAL LACUNAS CLOSE TO TABLE SINGULARITIES 174 3. CALCULATION OF THE
EVEN LOCAL PETROVSKII CLASS 182 4. CALCULATION OF THE ODD LOCAL
PETROVSKII CLASS 187 5. STABILIZATION OF LOCAL PETROVSKII CLASSES 191 6.
LOCAL LACUNAS CLOSE TO SIMPLE SINGULARITIES 192 7. GEOMETRIC
CHARACTERIZATION OF LOCAL LACUNAS AT SIMPLE SINGULARITIES 207 8. A
PROGRAM ENUMERATING TOPOLOGICALLY DISTINCT MORSIFICATIONS OF REAL
FUNCTION SINGULARITIES 209 CHAPTER VI. HOMOLOGY OF LOCAL SYSTEMS,
TWISTED MONODROMY THEORY, AND REGULARIZATION OF IMPROPER INTEGRATION
CYCLES 215 1. LOCAL SYSTEMS AND THEIR HOMOLOGY GROUPS 215 2. TWISTED
VANISHING HOMOLOGY OF FUNCTIONS AND COMPLETE INTERSECTIONS 218 3.
REGULARIZATION OF NON-COMPACT CYCLES 224 4. THE DOUBLE LOOP CYCLE 226
5. MONODROMY OF TWISTED VANISHING HOMOLOGY FOR PHAM SINGULARITIES 234
CONTENTS VII 6. STRATIFIED PICARD-LEFSCHETZ THEORY WITH TWISTED
COEFFICIENTS 240 CHAPTER VII. ANALYTIC PROPERTIES OF SURFACE POTENTIALS
251 1. INTRODUCTION 251 2. THEOREMS OF NEWTON AND IVORY 254 3.
HYPERBOLIC POTENTIALS ARE REGULAR IN THE HYPERBOLICITY DOMAIN (AFTER
V.I. ARNOLD AND A.B. GIVENTAL) 256 4. REDUCTION TO MONODROMY THEORY 260
5. RAMIFICATION OF POTENTIALS AND MONODROMY OF COMPLETE INTERSECTIONS
265 6. EXAMPLES: CURVES, QUADRICS, AND IVORY S SECOND THEOREM 272 7.
DESCRIPTION OF THE SMALL MONODROMY GROUP 274 8. PROOF OF THEOREM 1.4 283
9. PROOF OF THEOREM 1.3 284 CHAPTER VIII. MULTIDIMENSIONAL
HYPERGEOMETRIC FUNCTIONS, THEIR RAMIFICATION, SINGULARITIES, AND
RESONANCES 287 1. INTRODUCTION 287 2. PROOF OF THE MEROMORPHY THEOREM
291 3. THE HYPERGEOMETRIC FUNCTION AND ITS ONE-DIMENSIONAL
GENERALIZATIONS 295 4. HOMOLOGY OF COMPLEMENTS OF PLANE ARRANGEMENTS.
BASIC STRATA 297 5. THE NUMBER OF INDEPENDENT HYPERGEOMETRIC INTEGRALS
ON BASIC STRATA 305 BIBLIOGRAPHY 313 INDEX 321
|
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| indexdate | 2024-07-09T19:58:32Z |
| institution | BVB |
| isbn | 0821829483 |
| language | English |
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| physical | XI, 324 S. Ill. |
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| publisher | American Math. Soc. |
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| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Vasil'ev, V. A. Verfasser aut Applied Picard-Lefschetz theory V. A. Vassiliev Providence, RI American Math. Soc. 2002 XI, 324 S. Ill. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 97 Includes bibliographical references (p. 313-320) and index EQUAÇÕES DIFERENCIAIS PARCIAIS HIPERBÓLICAS larpcal FUNÇÕES DE VÁRIAS VARIÁVEIS COMPLEXAS larpcal GEOMETRIA ALGÉBRICA larpcal GRUPOS DE MONODROMIA larpcal SINGULARIDADES (GEOMETRIA ALGÉBRICA) larpcal TEORIA DE PICARD-LEFSCHETZ larpcal Integral representations Picard-Lefschetz theory Singularities (Mathematics) Picard-Lefschetz-Satz (DE-588)4760839-0 gnd rswk-swf Picard-Lefschetz-Satz (DE-588)4760839-0 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1324-8 Mathematical surveys and monographs 97 (DE-604)BV000018014 97 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012826540&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vasil'ev, V. A. Applied Picard-Lefschetz theory Mathematical surveys and monographs EQUAÇÕES DIFERENCIAIS PARCIAIS HIPERBÓLICAS larpcal FUNÇÕES DE VÁRIAS VARIÁVEIS COMPLEXAS larpcal GEOMETRIA ALGÉBRICA larpcal GRUPOS DE MONODROMIA larpcal SINGULARIDADES (GEOMETRIA ALGÉBRICA) larpcal TEORIA DE PICARD-LEFSCHETZ larpcal Integral representations Picard-Lefschetz theory Singularities (Mathematics) Picard-Lefschetz-Satz (DE-588)4760839-0 gnd |
| subject_GND | (DE-588)4760839-0 |
| title | Applied Picard-Lefschetz theory |
| title_auth | Applied Picard-Lefschetz theory |
| title_exact_search | Applied Picard-Lefschetz theory |
| title_full | Applied Picard-Lefschetz theory V. A. Vassiliev |
| title_fullStr | Applied Picard-Lefschetz theory V. A. Vassiliev |
| title_full_unstemmed | Applied Picard-Lefschetz theory V. A. Vassiliev |
| title_short | Applied Picard-Lefschetz theory |
| title_sort | applied picard lefschetz theory |
| topic | EQUAÇÕES DIFERENCIAIS PARCIAIS HIPERBÓLICAS larpcal FUNÇÕES DE VÁRIAS VARIÁVEIS COMPLEXAS larpcal GEOMETRIA ALGÉBRICA larpcal GRUPOS DE MONODROMIA larpcal SINGULARIDADES (GEOMETRIA ALGÉBRICA) larpcal TEORIA DE PICARD-LEFSCHETZ larpcal Integral representations Picard-Lefschetz theory Singularities (Mathematics) Picard-Lefschetz-Satz (DE-588)4760839-0 gnd |
| topic_facet | EQUAÇÕES DIFERENCIAIS PARCIAIS HIPERBÓLICAS FUNÇÕES DE VÁRIAS VARIÁVEIS COMPLEXAS GEOMETRIA ALGÉBRICA GRUPOS DE MONODROMIA SINGULARIDADES (GEOMETRIA ALGÉBRICA) TEORIA DE PICARD-LEFSCHETZ Integral representations Picard-Lefschetz theory Singularities (Mathematics) Picard-Lefschetz-Satz |
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