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Indices of vector fields and residues of singular holomorphic foliations:

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Bibliographic Details
Main Author:	Suwa, Tatsuo (Author)
Format:	Book
Language:	Undetermined
Published:	Paris Hermann 1998
Series:	Actualités mathématiques
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018420497&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Physical Description:	V, 204 S.
ISBN:	2705663614

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Record in the Search Index

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adam_text	TATSUO SUWA - PROFESSEUR A L UNIVERSITE D HOKKAIDO, JAPON INDICES OF VECTOR FIELDS AND RESIDUES OF SINGULAR HOLOMORPHIC FOLIATIONS ACTI AL1TES MATIIKMATIQLES HERMANN ^P EDITEURS DES SCIENCES ET DES ARTS CONTENTS CHAPTER I. BASIC MATERIAL 1. HOLOMORPHIC FUNCTIONS OF SEVERAL COMPLEX VARIABLES 1 2. THE RING OF GERMS OF HOLOMORPHIC FUNCTIONS 7 3. COMPLEX MANIFOLDS AND ANALYTIC VARIETIES 14 4. GERMS OF VARIETIES 21 5. VECTOR BUNDLES 24 6. VECTOR FIELDS AND DIFFERENTIAL FORMS 32 7. INTEGRATION OF DIFFERENTIAL FORMS 37 8. FROBENIUS THEOREM AND NON-SINGULAR FOLIATIONS 38 CHAPTER II. FURTHER TOPICS 1. DE RHAM COHOMOLOGY 43 2. CECH COHOMOLOGY 46 3. CECH-DE RHAM COHOMOLOGY AND DUALITY THEOREMS 47 4. INTEGRATION ALONG THE FIBER 57 5. THORN ISOMORPHISM AND THE EULER CLASS 60 6. BOCHNER-MARTINELLI KERNEL 66 7. CHERN-WEIL THEORY OF CHARACTERISTIC CLASSES 67 8. FURTHER TOPICS ON CONNECTIONS 70 9. VANISHING THEOREMS 74 10. GROTHENDIECK RESIDUES 78 11. DIVISORS 79 12. COHERENT SHEAVES 81 13. COMPLETE INTERSECTIONS AND LOCAL COMPLETE INTERSECTIONS 83 CHAPTER III. POINCARE-HOPF INDICES AND THE BAUM-BOTT RESIDUES OF HOLO- MORPHIC VECTOR FIELDS 1. INDEX THEOREM I 88 2. INDEX THEOREM II 92 3. LOCALIZATION OF CHARACTERISTIC CLASSES OF COMPLEX VECTOR BUNDLES 95 4. LOCALIZATION OF THE TOP CHERN CLASS 97 5. BAUM-BOTT RESIDUES OF HOLOMORPHIC VECTOR FIELDS 102 6. RESIDUES OF HOLOMORPHIC VECTOR FIELDS FOR VIRTUAL BUNDLES 108 7. ONE DIMENSIONAL SINGULAR FOLIATIONS 110 CONTENTS CHAPTER IV. INDICES AND RESIDUES OF VECTOR FIELDS ON SINGULAR VARIETIES 1. INDICES OF A VECTOR FIELD ON A SINGULAR VARIETY 114 2. CHARACTERISTIC NUMBERS ON SINGULAR VARIETIES 118 3. VIRTUAL INDICES AND APPLICATIONS 120 4. RESIDUES OF HOLOMORPHIC VECTOR FIELDS ON SINGULAR VARI- ETIES 125 5. RESIDUES FOR THE AMBIENT TANGENT BUNDLE 129 6. RESIDUES FOR THE NORMAL BUNDLE 131 7. RESIDUES FOR THE VIRTUAL TANGENT BUNDLE 135 8. GROTHENDIECK RESIDUES RELATIVE TO SUBVARIETIES AND EX- AMPLES 142 CHAPTER V. SINGULAR FOLIATIONS ON COMPLEX SURFACES 1. BAUM-BOTT RESIDUES OF SINGULAR FOLIATIONS ON COMPLEX SURFACES 148 2. CAMACHO-SAD INDEX AND GENERALIZATIONS 151 3. PROPERTIES OF THE GENERALIZED CAMACHO-SAD INDEX 157 4. GEOMETRIC INTERPRETATION OF THE INDEX 161 5. VARIATION AND ITS APPLICATIONS 162 6. SINGULAR FOLIATIONS DEFINED BY MEROMORPHIC FUNCTIONS 167 7. FOLIATIONS ARISING FROM POLYNOMIALS 172 CHAPTER VI. SINGULAR HOLOMORPHIC FOLIATIONS 1. SINGULAR FOLIATIONS ON COMPLEX MANIFOLDS 177 2. STRUCTURE OF THE SINGULAR SET 179 3. BAUM-BOTT RESIDUES 183 4. CHARACTERISTIC CLASSES ON SINGULAR VARIETIES 186 5. NASH RESIDUES 189 6. RESIDUES RELATIVE TO INVARIANT SUBVARIETIES 192 REFERENCES 199
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indexdate	2024-12-20T13:55:33Z
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spellingShingle	Suwa, Tatsuo Indices of vector fields and residues of singular holomorphic foliations
title	Indices of vector fields and residues of singular holomorphic foliations
title_auth	Indices of vector fields and residues of singular holomorphic foliations
title_exact_search	Indices of vector fields and residues of singular holomorphic foliations
title_full	Indices of vector fields and residues of singular holomorphic foliations Tatsuo Suwa
title_fullStr	Indices of vector fields and residues of singular holomorphic foliations Tatsuo Suwa
title_full_unstemmed	Indices of vector fields and residues of singular holomorphic foliations Tatsuo Suwa
title_short	Indices of vector fields and residues of singular holomorphic foliations
title_sort	indices of vector fields and residues of singular holomorphic foliations
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018420497&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT suwatatsuo indicesofvectorfieldsandresiduesofsingularholomorphicfoliations

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