Verfügbarkeit: Algebraic geometry

Algebraic geometry:

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Bibliographische Detailangaben
Hauptverfasser:	Görtz, Ulrich 1973- (VerfasserIn), Wedhorn, Torsten 1970- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Wiesbaden Vieweg + Teubner 2010-
Schriftenreihe:	Springer Studium Mathematik - Master
Schlagworte:	Algebraische Geometrie Lehrbuch
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	Ab Band 1, 2. Auflage im Verlag Wiesbaden : Springer Spektrum erschienen

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MARC


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Datensatz im Suchindex

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adam_text	EXERCISES 164 V CONTENTS INTRODUCTION 1 1 PREVARIETIES 7 AFFINE ALGEBRAIC SETS 8 AFFINE ALGEBRAIC SETS AS SPACES WITH FUNCTIONS 17 PREVARIETIES 22 PROJECTIVE VARIETIES 26 EXERCISES 35 2 SPECTRUM OF A RING 40 SPECTRUM OF A RING AS A TOPOLOGICAL SPACE 41 EXCURSION: SHEAVES 46 SPECTRUM OF A RING AS A LOCALLY RINGED SPACE 57 EXERCISES 62 3 SCHEMES 66 SCHEMES 66 EXAMPLES OF SCHEMES 72 BASIC PROPERTIES OF SCHEMES AND MORPHISMS OF SCHEMES 74 PREVARIETIES AS SCHEMES 78 SUBSCHEMES AND IMMERSIONS 83 EXERCISES 88 4 FIBER PRODUCTS 93 SCHEMES AS FUNCTORS 93 FIBER PRODUCTS OF SCHEMES 97 BASE CHANGE, FIBERS OF A MORPHISM 105 EXERCISES 114 5 SCHEMES OVER FIELDS 118 SCHEMES OVER A FIELD WHICH IS NOT ALGEBRAICALLY CLOSED 118 DIMENSION OF SCHEMES OVER A FIELD 120 SCHEMES OVER FIELDS AND EXTENSIONS OF THE BASE FIELD 133 INTERSECTIONS OF PLANE CURVES 138 EXERCISES 141 6 LOCAL PROPERTIES OF SCHEMES 145 THE TANGENT SPACE 146 SMOOTH MORPHISMS 153 REGULAR SCHEMES 158 NORMAL SCHEMES 161 BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/995886482 DIGITALISIERT DURCH VI CONTENTS 7 QUASI-COHERENT MODULES 169 EXCURSION: ?X- M DULES 169 QUASI-COHERENT MODULES ON A SCHEME 181 PROPERTIES OF QUASI-COHERENT MODULES 189 EXERCISES 199 8 REPRESENTABLE FUNCTORS 205 REPRESENTABLE FUNCTORS 206 THE EXAMPLE OF THE GRASSMANNIAN 209 BRAUER-SEVERI SCHEMES 219 EXERCISES 222 9 SEPARATED MORPHISMS 226 DIAGONAL OF SCHEME MORPHISMS AND SEPARATED MORPHISMS 226 RATIONAL MAPS AND FUNCTION FIELDS 232 EXERCISES 238 10 FINITENESS CONDITIONS 241 FINITENESS CONDITIONS (NOETHERIAN CASE) 242 FINITENESS CONDITIONS IN THE NON-NOETHERIAN CASE 249 SCHEMES OVER INDUCTIVE LIMITS OF RINGS 258 CONSTRUCTIBLE PROPERTIES 270 EXERCISES 278 11 VECTOR BUNDLES 286 VECTOR BUNDLES AND LOCALLY FREE MODULES 286 FLATTENING STRATIFICATION FOR MODULES 296 DIVISORS 298 VECTOR BUNDLES ON P 1 313 EXERCISES 316 12 AFFINE AND PROPER MORPHISMS 320 AFFINE MORPHISMS 320 FINITE AND QUASI-FINITE MORPHISMS 324 SERRE S AND CHEVALLEY S CRITERIA TO BE AFFINE 334 NORMALIZATION 339 PROPER MORPHISMS 343 ZARISKI S MAIN THEOREM 349 EXERCISE 602 VII 14 FLAT MORPHISMS AND DIMENSION 423 FLAT MORPHISMS 423 PROPERTIES OF FLAT MORPHISMS 429 FAITHFULLY FLAT DESCENT 439 DIMENSION AND FIBERS OF MORPHISMS 463 DIMENSION AND REGULARITY CONDITIONS 473 HUBERT SCHEMES 478 EXERCISES 480 15 ONE-DIMENSIONAL SCHEMES 485 MORPHISMS INTO AND FROM ONE-DIMENSIONAL SCHEMES 485 VALUATIVE CRITERIA 487 CURVES OVER FIELDS 491 DIVISORS ON CURVES 496 EXERCISES 500 16 EXAMPLES 503 DETERMINANTAL VARIETIES 503 CUBIC SURFACES AND A HUBERT MODULAR SURFACE 520 CYCLIC QUOTIENT SINGULARITIES 528 ABELIAN VARIETIES 532 EXERCISES 539 A THE LANGUAGE OF CATEGORIES 541 B COMMUTATIVE ALGEBRA 547 C PERMANENCE FOR PROPERTIES OF MORPHISMS OF SCHEMES 573 D RELATIONS BETWEEN PROPERTIES OF MORPHISMS OF SCHEMES 576 E CONSTRUCTIBLE AND OPEN PROPERTIES 578 BIBLIOGRAPHY 583 DETAILED LIST OF CONTENTS 588 INDEX OF SYMBOLS 598 INDEX
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spelling	Görtz, Ulrich 1973- Verfasser (DE-588)122267540 aut Algebraic geometry Ulrich Görtz, Torsten Wedhorn Wiesbaden Vieweg + Teubner 2010- txt rdacontent n rdamedia nc rdacarrier Springer Studium Mathematik - Master Ab Band 1, 2. Auflage im Verlag Wiesbaden : Springer Spektrum erschienen Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Algebraische Geometrie (DE-588)4001161-6 s DE-604 Wedhorn, Torsten 1970- Verfasser (DE-588)120349183 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018852610&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Görtz, Ulrich 1973- Wedhorn, Torsten 1970- Algebraic geometry Algebraische Geometrie (DE-588)4001161-6 gnd
subject_GND	(DE-588)4001161-6 (DE-588)4123623-3
title	Algebraic geometry
title_auth	Algebraic geometry
title_exact_search	Algebraic geometry
title_full	Algebraic geometry Ulrich Görtz, Torsten Wedhorn
title_fullStr	Algebraic geometry Ulrich Görtz, Torsten Wedhorn
title_full_unstemmed	Algebraic geometry Ulrich Görtz, Torsten Wedhorn
title_short	Algebraic geometry
title_sort	algebraic geometry
topic	Algebraische Geometrie (DE-588)4001161-6 gnd
topic_facet	Algebraische Geometrie Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018852610&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT gortzulrich algebraicgeometry AT wedhorntorsten algebraicgeometry

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