Verfügbarkeit: Positivity in algebraic geometry

Positivity in algebraic geometry:

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Lazarsfeld, Robert 1953- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin ; Heidelberg ; New York Springer [2004]
Schriftenreihe:	Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge
Schlagworte:	Algebraische Geometrie Positive Definitheit
Online-Zugang:	Inhaltsverzeichnis

Internformat

MARC


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Datensatz im Suchindex

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adam_text	CONTENTS NOTATION AND CONVENTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 PART ONE: AMPLE LINE BUNDLES AND LINEAR SERIES INTRODUCTION TO PART ONE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1 AMPLE AND NEF LINE BUNDLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.1 PRELIMINARIES: DIVISORS, LINE BUNDLES, AND LINEAR SERIES . . . . . . 7 1.1.A DIVISORS AND LINE BUNDLES . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.B LINEAR SERIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.1.C INTERSECTION NUMBERS AND NUMERICAL EQUIVALENCE . . . . . 15 1.1.D RIEMANNROCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2 THE CLASSICAL THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.2.A COHOMOLOGICAL PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.2.B NUMERICAL PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 1.2.C METRIC CHARACTERIZATIONS OF AMPLITUDE . . . . . . . . . . . . . . 39 1.3 Q -DIVISORS AND R -DIVISORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.3.A DEFINITIONS FOR Q -DIVISORS . . . . . . . . . . . . . . . . . . . . . . . . . . 44 1.3.B R -DIVISORS AND THEIR AMPLITUDE . . . . . . . . . . . . . . . . . . . . 48 1.4 NEF LINE BUNDLES AND DIVISORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 1.4.A DEFINITIONS AND FORMAL PROPERTIES . . . . . . . . . . . . . . . . . . . 51 1.4.B KLEIMAN S THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 1.4.C CONES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 1.4.D FUJITA S VANISHING THEOREM . . . . . . . . . . . . . . . . . . . . . . . . 65 1.5 EXAMPLES AND COMPLEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 1.5.A RULED SURFACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 1.5.B PRODUCTS OF CURVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 1.5.C ABELIAN VARIETIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 1.5.D OTHER VARIETIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 1.5.E LOCAL STRUCTURE OF THE NEF CONE . . . . . . . . . . . . . . . . . . . . 82 XII CONTENTS 1.5.F THE CONE THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 1.6 INEQUALITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 1.6.A GLOBAL RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 1.6.B MIXED MULTIPLICITIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 1.7 AMPLITUDE FOR A MAPPING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 1.8 CASTELNUOVOMUMFORD REGULARITY. . . . . . . . . . . . . . . . . . . . . . . . . . 98 1.8.A DEFINITIONS, FORMAL PROPERTIES, AND VARIANTS . . . . . . . . . . 99 1.8.B REGULARITY AND COMPLEXITY . . . . . . . . . . . . . . . . . . . . . . . . . 107 1.8.C REGULARITY BOUNDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 1.8.D SYZYGIES OF ALGEBRAIC VARIETIES . . . . . . . . . . . . . . . . . . . . . . 115 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 2 LINEAR SERIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 2.1 ASYMPTOTIC THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 2.1.A BASIC DEFINITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 2.1.B SEMIAMPLE LINE BUNDLES . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 2.1.C IITAKA FIBRATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 2.2 BIG LINE BUNDLES AND DIVISORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 2.2.A BASIC PROPERTIES OF BIG DIVISORS . . . . . . . . . . . . . . . . . . . . 139 2.2.B PSEUDOEECTIVE AND BIG CONES . . . . . . . . . . . . . . . . . . . . . . 145 2.2.C VOLUME OF A BIG DIVISOR . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 2.3 EXAMPLES AND COMPLEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 2.3.A ZARISKI S CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 2.3.B CUTKOSKY S CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 2.3.C BASE LOCI OF NEF AND BIG LINEAR SERIES . . . . . . . . . . . . . . 164 2.3.D THE THEOREM OF CAMPANA AND PETERNELL . . . . . . . . . . . . . 166 2.3.E ZARISKI DECOMPOSITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 2.4 GRADED LINEAR SERIES AND FAMILIES OF IDEALS . . . . . . . . . . . . . . . . . 172 2.4.A GRADED LINEAR SERIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 2.4.B GRADED FAMILIES OF IDEALS . . . . . . . . . . . . . . . . . . . . . . . . . . 176 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 3 GEOMETRIC MANIFESTATIONS OF POSITIVITY . . . . . . . . . . . . . . . . . . . . 185 3.1 THE LEFSCHETZ THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 3.1.A TOPOLOGY OF ANE VARIETIES . . . . . . . . . . . . . . . . . . . . . . . . 186 3.1.B THE THEOREM ON HYPERPLANE SECTIONS . . . . . . . . . . . . . . . 192 3.1.C HARD LEFSCHETZ THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 3.2 PROJECTIVE SUBVARIETIES OF SMALL CODIMENSION . . . . . . . . . . . . . . . 201 3.2.A BARTH S THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 3.2.B HARTSHORNE S CONJECTURES . . . . . . . . . . . . . . . . . . . . . . . . . . 204 3.3 CONNECTEDNESS THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 3.3.A BERTINI THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 3.3.B THEOREM OF FULTON AND HANSEN . . . . . . . . . . . . . . . . . . . . . 210 3.3.C GROTHENDIECK S CONNECTEDNESS THEOREM . . . . . . . . . . . . . 212 3.4 APPLICATIONS OF THE FULTONHANSEN THEOREM . . . . . . . . . . . . . . . . 213 3.4.A SINGULARITIES OF MAPPINGS . . . . . . . . . . . . . . . . . . . . . . . . . . 214 CONTENTS XIII 3.4.B ZAK S THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 3.4.C ZARISKI S PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 3.5 VARIANTS AND EXTENSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 3.5.A HOMOGENEOUS VARIETIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 3.5.B HIGHER CONNECTIVITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 4 VANISHING THEOREMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 4.1 PRELIMINARIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 4.1.A NORMAL CROSSINGS AND RESOLUTIONS OF SINGULARITIES . . . . . 240 4.1.B COVERING LEMMAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 4.2 KODAIRA AND NAKANO VANISHING THEOREMS . . . . . . . . . . . . . . . . . . 248 4.3 VANISHING FOR BIG AND NEF LINE BUNDLES . . . . . . . . . . . . . . . . . . . . 252 4.3.A STATEMENT AND PROOF OF THE THEOREM . . . . . . . . . . . . . . . . 252 4.3.B SOME APPLICATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 4.4 GENERIC VANISHING THEOREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267 5 LOCAL POSITIVITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 5.1 SESHADRI CONSTANTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 5.2 LOWER BOUNDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 5.2.A BACKGROUND AND STATEMENTS . . . . . . . . . . . . . . . . . . . . . . . . 278 5.2.B MULTIPLICITIES OF DIVISORS IN FAMILIES . . . . . . . . . . . . . . . . . 282 5.2.C PROOF OF THEOREM 5.2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 5.3 ABELIAN VARIETIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290 5.3.A PERIOD LENGTHS AND SESHADRI CONSTANTS . . . . . . . . . . . . . . 290 5.3.B PROOF OF THEOREM 5.3.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 5.3.C COMPLEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 5.4 LOCAL POSITIVITY ALONG AN IDEAL SHEAF . . . . . . . . . . . . . . . . . . . . . . 303 5.4.A DEFINITION AND FORMAL PROPERTIES OF THE S-INVARIANT . . . . 303 5.4.B COMPLEXITY BOUNDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 NOTES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 APPENDICES A PROJECTIVE BUNDLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 B COHOMOLOGY AND COMPLEXES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 B.1 COHOMOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 B.2 COMPLEXES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 GLOSSARY OF NOTATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 CONTENTS OF VOLUME II NOTATION AND CONVENTIONS II : 1 PART TWO: POSITIVITY FOR VECTOR BUNDLES INTRODUCTION TO PART TWO II : 5 6 AMPLE AND NEF VECTOR BUNDLES II : 7 6.1 CLASSICAL THEORY II : 7 6.1.A DEFINITION AND FIRST PROPERTIES II : 8 6.1.B COHOMOLOGICAL PROPERTIES II : 11 6.1.C CRITERIA FOR AMPLITUDE II : 15 6.1.D METRIC APPROACHES TO POSITIVITY OF VECTOR BUNDLES II : 18 6.2 Q -TWISTED AND NEF BUNDLES II : 20 6.2.A TWISTS BY Q -DIVISORS II : 20 6.2.B NEF BUNDLES II : 24 6.3 EXAMPLES AND CONSTRUCTIONS II : 27 6.3.A NORMAL AND TANGENT BUNDLES II : 27 6.3.B AMPLE COTANGENT BUNDLES AND HYPERBOLICITY II : 36 6.3.C PICARD BUNDLES II : 44 6.3.D THE BUNDLE ASSOCIATED TO A BRANCHED COVERING II : 47 6.3.E DIRECT IMAGES OF CANONICAL BUNDLES II : 51 6.3.F SOME CONSTRUCTIONS OF POSITIVE VECTOR BUNDLES II : 53 6.4 AMPLE VECTOR BUNDLES ON CURVES II : 56 6.4.A REVIEW OF SEMISTABILITY II : 57 6.4.B SEMISTABILITY AND AMPLITUDE II : 60 NOTES II : 64 7 GEOMETRIC PROPERTIES OF AMPLE BUNDLES II : 65 7.1 TOPOLOGY II : 65 7.1.A SOMMESE S THEOREM II : 65 XVI CONTENTS OF VOLUME II 7.1.B THEOREM OF BLOCH AND GIESEKER II : 68 7.1.C A BARTH-TYPE THEOREM FOR BRANCHED COVERINGS II : 71 7.2 DEGENERACY LOCI II : 74 7.2.A STATEMENTS AND FIRST EXAMPLES II : 74 7.2.B PROOF OF CONNECTEDNESS OF DEGENERACY LOCI II : 78 7.2.C SOME APPLICATIONS II : 82 7.2.D VARIANTS AND EXTENSIONS II : 87 7.3 VANISHING THEOREMS II : 89 7.3.A VANISHING THEOREMS OF GRITHS AND LE POTIER II : 89 7.3.B GENERALIZATIONS II : 95 NOTES II : 98 8 NUMERICAL PROPERTIES OF AMPLE BUNDLES II : 101 8.1 PRELIMINARIES FROM INTERSECTION THEORY II : 101 8.1.A CHERN CLASSES FOR Q -TWISTED BUNDLES II : 102 8.1.B CONE CLASSES II : 104 8.1.C CONE CLASSES FOR Q -TWISTS II : 110 8.2 POSITIVITY THEOREMS II : 111 8.2.A POSITIVITY OF CHERN CLASSES II : 111 8.2.B POSITIVITY OF CONE CLASSES II : 114 8.3 POSITIVE POLYNOMIALS FOR AMPLE BUNDLES II : 117 8.4 SOME APPLICATIONS II : 125 8.4.A POSITIVITY OF INTERSECTION PRODUCTS II : 125 8.4.B NON-EMPTINESS OF DEGENERACY LOCI II : 127 8.4.C SINGULARITIES OF HYPERSURFACES ALONG A CURVE II : 129 NOTES II : 132 PART THREE: MULTIPLIER IDEALS AND THEIR APPLICATIONS INTRODUCTION TO PART THREE II : 135 9 MULTIPLIER IDEAL SHEAVES II : 139 9.1 PRELIMINARIES II : 140 9.1.A Q -DIVISORS II : 140 9.1.B NORMAL CROSSING DIVISORS AND LOG RESOLUTIONS II : 142 9.1.C THE KAWAMATAVIEHWEG VANISHING THEOREM II : 147 9.2 DEFINITION AND FIRST PROPERTIES II : 151 9.2.A DEFINITION OF MULTIPLIER IDEALS II : 152 9.2.B FIRST PROPERTIES II : 158 9.3 EXAMPLES AND COMPLEMENTS II : 162 9.3.A MULTIPLIER IDEALS AND MULTIPLICITY II : 162 9.3.B INVARIANTS ARISING FROM MULTIPLIER IDEALS II : 165 9.3.C MONOMIAL IDEALS II : 170 9.3.D ANALYTIC CONSTRUCTION OF MULTIPLIER IDEALS II : 176 CONTENTS OF VOLUME II XVII 9.3.E ADJOINT IDEALS II : 179 9.3.F MULTIPLIER AND JACOBIAN IDEALS II : 181 9.3.G MULTIPLIER IDEALS ON SINGULAR VARIETIES II : 182 9.4 VANISHING THEOREMS FOR MULTIPLIER IDEALS II : 185 9.4.A LOCAL VANISHING FOR MULTIPLIER IDEALS II : 186 9.4.B THE NADEL VANISHING THEOREM II : 188 9.4.C VANISHING ON SINGULAR VARIETIES II : 191 9.4.D NADEL S THEOREM IN THE ANALYTIC SETTING II : 192 9.4.E NON-VANISHING AND GLOBAL GENERATION II : 193 9.5 GEOMETRIC PROPERTIES OF MULTIPLIER IDEALS II : 195 9.5.A RESTRICTIONS OF MULTIPLIER IDEALS II : 195 9.5.B SUBADDITIVITY II : 201 9.5.C THE SUMMATION THEOREM II : 204 9.5.D MULTIPLIER IDEALS IN FAMILIES II : 210 9.5.E COVERINGS II : 213 9.6 SKODA S THEOREM II : 216 9.6.A INTEGRAL CLOSURE OF IDEALS II : 216 9.6.B SKODA S THEOREM: STATEMENTS II : 221 9.6.C SKODA S THEOREM: PROOFS II : 226 9.6.D VARIANTS II : 228 NOTES II : 230 10 SOME APPLICATIONS OF MULTIPLIER IDEALS II : 233 10.1 SINGULARITIES II : 233 10.1.A SINGULARITIES OF PROJECTIVE HYPERSURFACES II : 233 10.1.B SINGULARITIES OF THETA DIVISORS II : 235 10.1.C A CRITERION FOR SEPARATION OF JETS OF ADJOINT SERIES II : 238 10.2 MATSUSAKA S THEOREM II : 239 10.3 NAKAMAYE S THEOREM ON BASE LOCI II : 246 10.4 GLOBAL GENERATION OF ADJOINT LINEAR SERIES II : 251 10.4.A FUJITA CONJECTURE AND ANGEHRN*SIU THEOREM II : 252 10.4.B LOCI OF LOG-CANONICAL SINGULARITIES II : 254 10.4.C PROOF OF THE THEOREM OF ANGEHRN AND SIU II : 258 10.5 THE EECTIVE NULLSTELLENSATZ II : 262 NOTES II : 267 11 ASYMPTOTIC CONSTRUCTIONS II : 269 11.1 CONSTRUCTION OF ASYMPTOTIC MULTIPLIER IDEALS II : 270 11.1.A COMPLETE LINEAR SERIES II : 270 11.1.B GRADED SYSTEMS OF IDEALS AND LINEAR SERIES II : 276 11.2 PROPERTIES OF ASYMPTOTIC MULTIPLIER IDEALS II : 282 11.2.A LOCAL STATEMENTS II : 282 11.2.B GLOBAL RESULTS II : 285 11.2.C MULTIPLICATIVITY OF PLURIGENERA II : 292 11.3 GROWTH OF GRADED FAMILIES AND SYMBOLIC POWERS II : 293 XVIII CONTENTS OF VOLUME II 11.4 FUJITA S APPROXIMATION THEOREM II : 299 11.4.A STATEMENT AND FIRST CONSEQUENCES II : 299 11.4.B PROOF OF FUJITA S THEOREM II : 305 11.4.C THE DUAL OF THE PSEUDOEECTIVE CONE II : 307 11.5 SIU S THEOREM ON PLURIGENERA II : 312 NOTES II : 320 REFERENCES II : 323 GLOSSARY OF NOTATION II : 357 INDEX II : 363
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author	Lazarsfeld, Robert 1953-
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discipline	Mathematik
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id	DE-604.BV019407694
illustrated	Not Illustrated
indexdate	2024-07-09T19:59:36Z
institution	BVB
language	English
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publishDate	2004
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series2	Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge
spelling	Lazarsfeld, Robert 1953- Verfasser (DE-588)102154279 aut Positivity in algebraic geometry Robert Lazarsfeld Berlin ; Heidelberg ; New York Springer [2004] txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Positive Definitheit (DE-588)4382343-9 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Positive Definitheit (DE-588)4382343-9 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012869758&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Lazarsfeld, Robert 1953- Positivity in algebraic geometry Algebraische Geometrie (DE-588)4001161-6 gnd Positive Definitheit (DE-588)4382343-9 gnd
subject_GND	(DE-588)4001161-6 (DE-588)4382343-9
title	Positivity in algebraic geometry
title_auth	Positivity in algebraic geometry
title_exact_search	Positivity in algebraic geometry
title_full	Positivity in algebraic geometry Robert Lazarsfeld
title_fullStr	Positivity in algebraic geometry Robert Lazarsfeld
title_full_unstemmed	Positivity in algebraic geometry Robert Lazarsfeld
title_short	Positivity in algebraic geometry
title_sort	positivity in algebraic geometry
topic	Algebraische Geometrie (DE-588)4001161-6 gnd Positive Definitheit (DE-588)4382343-9 gnd
topic_facet	Algebraische Geometrie Positive Definitheit
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012869758&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT lazarsfeldrobert positivityinalgebraicgeometry

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