Algebraic surfaces and holomorphic vector bundles:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1998
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 328 S. |
| ISBN: | 0387983619 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804126471342522368 |
|---|---|
| adam_text | ROBERT FRIEDMAN ALGEBRAIC SURFACES AND HOLOMORPHIC VECTOR BUNDLES
SPRINGER CONTENTS PREFACE V INTRODUCTION 1 1 CURVES ON A SURFACE 7
INTRODUCTION 7 INVARIANTS OF A SURFACE 8 DIVISORS ON A SURFACE 9
ADJUNCTION AND ARITHMETIC GENUS 13 THE RIEMANN-ROCH FORMULA 15 ALGEBRAIC
PROOF OF THE HODGE INDEX THEOREM 16 AMPLE AND NEF DIVISORS 18 EXERCISES
22 2 COHERENT SHEAVES 25 WHAT IS A COHERENT SHEAF? 25 A RAPID REVIEW OF
CHERN CLASSES FOR PROJECTIVE VARIETIES 27 RANK 2 BUNDLES AND SUB-LINE
BUNDLES 31 ELEMENTARY MODIFICATIONS 41 SINGULARITIES OF COHERENT SHEAVES
42 TORSION FREE AND REFLEXIVE SHEAVES 43 DOUBLE COVERS 46 APPENDIX: SOME
COMMUTATIVE ALGEBRA 51 EXERCISES 54 3 BIRATIONAL GEOMETRY 59 BLOWING UP
59 THE CASTELNUOVO CRITERION AND FACTORIZATION OF BIRATIONAL MORPHISMS
64 MINIMAL MODELS 70 VIII CONTENTS MORE GENERAL CONTRACTIONS 72
EXERCISES 79 4 STABILITY 85 DEFINITION OF MUMFORD-TAKEMOTO STABILITY 85
EXAMPLES FOR CURVES 89 SOME EXAMPLES OF STABLE BUNDLES ON P 2 91
GIESEKER STABILITY 96 UNSTABLE AND SEMISTABLE SHEAVES 97 CHANGE OF
POLARIZATION 99 THE DIFFERENTIAL GEOMETRY OF STABLE VECTOR BUNDLES 101
EXERCISES 108 5 SOME EXAMPLES OF SURFACES 113 RATIONAL RULED SURFACES
113 GENERAL RULED SURFACES 117 LINEAR SYSTEMS OF CUBICS 125 AN
INTRODUCTION TO KZ SURFACES 132 EXERCISES 137 6 VECTOR BUNDLES OVER
RULED SURFACES 141 SUITABLE AMPLE DIVISORS 141 RULED SURFACES 149 A
BRIEF INTRODUCTION TO LOCAL AND GLOBAL MODULI 153 A ZARISKI OPEN SUBSET
OF THE MODULI SPACE 159 EXERCISES 163 7 AN INTRODUCTION TO ELLIPTIC
SURFACES 167 SINGULAR FIBERS 167 SINGULAR FIBERS OF ELLIPTIC FIBRATIONS
172 INVARIANTS AND THE CANONICAL BUNDLE FORMULA 175 ELLIPTIC SURFACES
WITH A SECTION AND WEIERSTRASS MODELS 178 MORE GENERAL ELLIPTIC SURFACES
183 THE FUNDAMENTAL GROUP 188 EXERCISES 190 8 VECTOR BUNDLES OVER
ELLIPTIC SURFACES 197 STABLE BUNDLES ON SINGULAR CURVES 197 STABLE
BUNDLES OF ODD FIBER DEGREE OVER ELLIPTIC SURFACES 200 A ZARISKI OPEN
SUBSET OF THE MODULI SPACE 203 AN OVERVIEW OF DONALDSON INVARIANTS 205
THE 2-DIMENSIONAL INVARIANT 209 CONTENTS IX MODULI SPACES VIA EXTENSIONS
217 VECTOR BUNDLES WITH TRIVIAL DETERMINANT 225 EVEN FIBER DEGREE AND
MULTIPLE FIBERS 237 EXERCISES 240 9 BOGOMOLOV S INEQUALITY AND
APPLICATIONS 245 STATEMENT OF THE THEOREM 245 THE THEOREMS OF BOMBIERI
AND REIDER 248 THE PROOF OF BOGOMOLOV S THEOREM 252 SYMMETRIC POWERS OF
VECTOR BUNDLES ON CURVES 257 RESTRICTION THEOREMS 260 APPENDIX: GALOIS
DESCENT THEORY 265 EXERCISES 274 10 CLASSIFICATION OF ALGEBRAIC SURFACES
AND OF STABLE BUNDLES 277 OUTLINE OF THE CLASSIFICATION OF SURFACES 277
PROOF OF CASTELNUOVO S THEOREM 284 THE ALBANESE MAP 288 PROOFS OF THE
CLASSIFICATION THEOREMS FOR SURFACES 290 THE CASTELNUOVO-DEFRANCHIS
THEOREM 302 CLASSIFICATION OF THREEFOLDS 305 CLASSIFICATION OF VECTOR
BUNDLES 307 EXERCISES 313 REFERENCES 315 INDEX 323
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.35 |
| dewey-search | 515/.35 |
| dewey-sort | 3515 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011885351 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:17:59Z |
| institution | BVB |
| isbn | 0387983619 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008030138 |
| oclc_num | 37588525 |
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| owner_facet | DE-29 DE-29T DE-384 DE-355 DE-BY-UBR DE-739 DE-703 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
| physical | IX, 328 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Friedman, Robert Verfasser aut Algebraic surfaces and holomorphic vector bundles Robert Friedman New York [u.a.] Springer 1998 IX, 328 S. txt rdacontent n rdamedia nc rdacarrier Universitext Algebraïsche oppervlakken gtt Fibrés vectoriels ram Holomorfe functies gtt Surfaces algébriques ram Vectorbundels gtt Surfaces, Algebraic Vector bundles Algebraische Fläche (DE-588)4195660-6 gnd rswk-swf Vektorraumbündel (DE-588)4187470-5 gnd rswk-swf Vektorraumbündel (DE-588)4187470-5 s Algebraische Fläche (DE-588)4195660-6 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008030138&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Friedman, Robert Algebraic surfaces and holomorphic vector bundles Algebraïsche oppervlakken gtt Fibrés vectoriels ram Holomorfe functies gtt Surfaces algébriques ram Vectorbundels gtt Surfaces, Algebraic Vector bundles Algebraische Fläche (DE-588)4195660-6 gnd Vektorraumbündel (DE-588)4187470-5 gnd |
| subject_GND | (DE-588)4195660-6 (DE-588)4187470-5 |
| title | Algebraic surfaces and holomorphic vector bundles |
| title_auth | Algebraic surfaces and holomorphic vector bundles |
| title_exact_search | Algebraic surfaces and holomorphic vector bundles |
| title_full | Algebraic surfaces and holomorphic vector bundles Robert Friedman |
| title_fullStr | Algebraic surfaces and holomorphic vector bundles Robert Friedman |
| title_full_unstemmed | Algebraic surfaces and holomorphic vector bundles Robert Friedman |
| title_short | Algebraic surfaces and holomorphic vector bundles |
| title_sort | algebraic surfaces and holomorphic vector bundles |
| topic | Algebraïsche oppervlakken gtt Fibrés vectoriels ram Holomorfe functies gtt Surfaces algébriques ram Vectorbundels gtt Surfaces, Algebraic Vector bundles Algebraische Fläche (DE-588)4195660-6 gnd Vektorraumbündel (DE-588)4187470-5 gnd |
| topic_facet | Algebraïsche oppervlakken Fibrés vectoriels Holomorfe functies Surfaces algébriques Vectorbundels Surfaces, Algebraic Vector bundles Algebraische Fläche Vektorraumbündel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008030138&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT friedmanrobert algebraicsurfacesandholomorphicvectorbundles |