Verfügbarkeit: Graded algebras in algebraic geometry

Graded algebras in algebraic geometry:

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Bibliographische Detailangaben
Hauptverfasser:	Simis, Aron 1942- (VerfasserIn), Ramos, Zaqueu (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Berlin De Gruyter [2022]
Schriftenreihe:	De Gruyter expositions in mathematics volume 70
Schlagworte:	Algebraische Geometrie Kommutative Algebra Graduierter Ring Graduierter Modul Schnitt <Mathematik>
Online-Zugang:	https://www.degruyter.com/isbn/9783110637540 Inhaltsverzeichnis Inhaltsverzeichnis
Beschreibung:	XV, 445 Seiten 24 cm, 876 g
ISBN:	9783110637540 3110637545

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MARC


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Datensatz im Suchindex

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adam_text	CONTENTS ACKNOWLEDGMENTS - VII FOREWORD - IX 1 1.1 1.2 1.2.1 1.2.2 1.3 1.4 GEOMETRIC MOTIVATION - 1 BITS FROM INTERSECTION THEORY - 1 CORRESPONDENCES AND INCIDENCE VARIETIES - 4 EXAMPLES ---- 4 ALGEBRAIC COUNTERPART - 6 RULED JOINS ---- 7 EXERCISES - 10 2 2.1 2.2 2.2.1 2.2.2 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.4 GRADED ALGEBRAS - 13 ARBITRARY GRADINGS - 13 NOTABLE BIGRADED ALGEBRAS - 16 THE SYMMETRIC ALGEBRA - 16 OTHER BIGRADED ALGEBRAS - 18 STANDARD GRADED ALGEBRAS - 18 REES ALGEBRAS OF IDEALS - 18 REES ALGEBRAS OF MODULES ---- 28 COMPLEMENTS ON THE FIBER CONE - 36 COHOMOLOGICAL INVARIANTS - 39 EXERCISES - 41 3 3.1 3.1.1 3.1.2 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.3 3.3.1 3.3.2 3.4 3.4.1 3.4.2 RATIONAL MAPS, 1 - 47 BASICS OF RATIONAL MAPS - 47 TERMINOLOGY - 47 BASIC PROPERTIES - 48 A CHARACTERISTIC-FREE CRITERION OF BIRATIONALITY - 50 PROLEGOMENA: THE KOSZUL-HILBERT LEMMA - 50 PRELIMINARIES ON RATIONAL MAPS ON REDUCED VARIETIES - 51 THE JACOBIAN DUAL RANK VERSUS BIRATIONALITY - 59 STATEMENT AND PROOF OF THE CRITERION - 63 A ROLE OF SYZYGIES ---- 67 BIRATIONAL COMBINATORICS - 70 THE UNDERLYING ARITHMETIC - 71 MONOMIAL BIRATIONAL MAPS IN DEGREE TWO - 73 ON THE DEGREE OF A RATIONAL MAP - 77 BASIC INGREDIENTS - 77 DEGREE UPPER BOUNDS - 81 XII CONTENTS 3.5 EXERCISES ----- 85 4 RATIONAL MAPS, II - 89 4.1 COMPLEMENTS ON THE BASE IDEAL ----89 4.1.1 DEGREE SEQUENCES - 89 4.1.2 THE SEMILINEAR RELATION TYPE ------92 4.2 INVERSION FACTORS OF BIRATIONAL MAPS ---- 93 4.2.1 BASIC LANDSCAPE ---- 94 4.2.2 RELATION TO SYMBOLIC POWERS ------- 96 4.3 NEWTON COMPLEMENTARY DUAL ------- 97 4.3.1 PRELIMINARIES ---- 97 4.3.2 MAIN RESULTS ---- 99 4.3.3 RELATION TO THE GRAPH OF A RATIONAL MAP ---- 104 4.4 ELEMENTS OF RATIONAL MAPS OVER A GROUND RING ---- 108 4.4.1 ALGEBRAIC DATA ---- 108 4.4.2 RATIONAL MAPS AND REPRESENTATIVES ----- 110 4.4.3 DEGREE UNDER SPECIALIZATION ---- 113 4.5 EXERCISES ---- 115 5 THE GRADIENT IDEAL - 119 5.1 THE UNDERLYING GEOMETRY ----- 119 5.1.1 LINEAR TYPE ---- 120 5.1.2 HYPERPLANE ARRANGEMENTS ---- 121 5.1.3 BEHAVIOR ALONG A FAMILY ----- 129 5.2 FREE DIVISORS ----- 140 5.2.1 GENERAL NONSENSE ---- 140 5.2.2 ALGEBRAIC LOGARITHMIC VECTOR FIELDS ----- 141 5.2.3 FAMILIES OF FREE DIVISORS ----- 145 5.2.4 WEIGHTED HOMOGENEOUS DIVISORS ---- 148 5.3 EXERCISES ----- 155 6 CREMONA TRANSFORMATIONS, I - 159 6.1 PLANE CREMONA TRANSFORMATIONS: HOMALOIDAL NETS ---- 159 6.1.1 WEIGHTED CLUSTER OF BASE POINTS ---- 159 6.1.2 RELATION TO FAT IDEALS ---- 163 6.1.3 FROM FAT IDEALS BACK TO THE CREMONA BASE IDEAL - 172 6.1.4 PROPER HOMALOIDAL TYPES WITH LARGE HIGHEST VIRTUAL MULTIPLICITY ---- 173 6.2 PLANE CREMONA TRANSFORMATIONS: SUBHOMALOIDAL TYPES - 179 6.2.1 ARITHMETIC QUADRATIC TRANSFORMATIONS ACTING ON FAT POINTS ---- 179 6.2.2 SUBHOMALOIDAL MULTIPLICITY SETS ----- 181 6.2.3 3-UNIFORM SUBHOMALOIDAL TYPES ----- 183 6.2.4 MAIN THEOREM ---- 199 CONTENTS - XIII 6.2.5 6.3 7 7.1 7.1.1 7.1.2 7.1.3 7.1.4 7.1.5 7.2 7.2.1 7.2.2 7.2.3 7.3 7.3.1 7.3.2 7.3.3 7.4 8 8.1 8.2 8.3 8.3.1 8.3.2 8.3.3 8.4 8.4.1 8.4.2 8.5 8.6 8.7 9 9.1 9.1.1 9.1.2 9.1.3 9.2 RELATION TO BORDIGA-WHITE PARAMETRIZATIONS ---- 203 EXERCISES ---- 206 CREMONA TRANSFORMATIONS, II - 209 GENERALIZED DE JONQUIERES TRANSFORMATIONS ---- 209 FULLY DOWNGRADED SEQUENCES - 211 GENERALIZED DE JONQUIERES TRANSFORMATIONS ---- 213 GENERALIZED DE JONQUIERES TRANSFORMATIONS UNDER NEWTON DUALITY ---- 215 GENERALIZED DE JONQUIERES TRANSFORMATIONS WITH IDENTITY SUPPORT ---- 218 THE MINIMAL FREE RESOLUTION OF THE BASE IDEAL ---- 218 THE GRAPH (BLOWUP) OF A CREMONA MAP ---- 220 THE GRAPH OF A DE JONQUIERES MAP WITH IDENTITY SUPPORT ---- 220 CREMONA MAPS WITH A COHEN-MACAULAY GRAPH ---- 227 CREMONA MAPS AND SYMBOLIC REES ALGEBRAS - 231 MONOMIAL CREMONA TRANSFORMATIONS ---- 235 THE GROUP OF MONOMIAL CREMONA TRANSFORMATIONS ---- 235 MONOMIAL CREMONA TRANSFORMATIONS OF DEGREE 2 ---- 243 A DUALITY PRINCIPLE ---- 256 EXERCISES ---- 259 STEPS IN ELIMINATION - 263 ELIMINATION ALGEBRAS ---- 263 IMPLICITIZATION ---- 266 DE JONQUIERES LIKE IMPLICITIZATION ---- 267 ALGEBRAIC PRELIMS ---- 267 THE (/F,G)-PARAMETRIZATION ---- 268 THE EQUATIONS OF THE REES ALGEBRA ---- 273 IMPLICITIZATION IN DIMENSION 1 ---- 278 DIMENSION ZERO ---- 278 DIMENSION ONE ---- 293 THE CLASSICAL RESULTANT ---- 295 ELIMINATING FROM CORRESPONDENCES ---- 297 EXERCISES ---- 300 THE GAUSS MAP - 303 GAUSS IMAGE OF HIGHER ORDER ---- 303 NOTABLE CASES. I: THE ORDINARY GAUSS IMAGE ---- 305 NOTABLE CASES. II: THE DUAL VARIETY ---- 306 RELATION TO THE TANGENTIAL VARIETY ---- 308 THE GAUSS IMAGE OF A UNIRATIONAL VARIETY ---- 310 XIV CONTENTS 9.2.1 THE ALGEBRAIC STRUCTURAL DATA - 310 9.2.2 THE GAUSS IMAGE OF TORIC VARIETIES ---- 313 9.2.3 ALGEBRAS OF VERONESE TYPE - 314 9.3 ABSTRACT GAUSS MAPS ---- 316 9.4 THE GEOMETRY OF THE ANALYTIC SPREAD ---- 317 9.4.1 MAXIMAL ANALYTIC SPREAD - 317 9.4.2 ANALYTIC SPREAD VERSUS THE FITTING IDEAL ---- 322 9.4.3 CASE STUDY: THE MODULE OF DIFFERENTIALS - 323 9.4.4 MAIN THEOREM OF ABSTRACT GAUSS MAPS ---- 325 9.5 EXERCISES ----- 329 10 TANGENT VARIETIES ---- 333 10.1 ALGEBRAIC FULTON-HANSEN THEOREMS ----- 333 10.1.1 ALGEBRAIC PRELIMINARIES - 333 10.1.2 THE UNDERLYING GEOMETRY ---- 337 10.1.3 THE TANGENTIAL VARIETY TO A UNIRATIONAL VARIETY - 340 10.2 REFINED PROPERTIES OF TANGENT ALGEBRAS - 341 10.2.1 EXPECTED STAR DIMENSION ---- 343 10.2.2 SET THEORETIC STARLIKE LINEARITY ----- 347 10.2.3 STARLIKE LINEARITY - 348 10.2.4 BEHAVIOR UNDER FLAT DEFORMATION - 351 10.2.5 A GLIMPSE OF THE BLOWUP OF THE KAHLER DIFFERENTIALS ---- 354 10.3 EXERCISES ----- 356 11 EMBEDDED JOINSAND SECANTS - 359 11.1 JOINS ---- 359 11.1.1 ALGEBRAIC SIDE ----- 359 11.1.2 THE GEOMETRIC BACKGROUND ----- 360 11.1.3 RELATION TO THE BAYER-MUMFORD DEFORMATION - 363 11.1.4 THE EMBEDDED JOIN OF A UNION OF LINEAR SPACES - 366 11.1.5 INITIAL DEGREE OF A JOIN - 368 11.2 SECANTS ----- 369 11.2.1 SECANTS OF DETERMINANTALAND PFAFFIAN SCHEMES - 370 11.2.2 SECANTS OFVARIETIES CUT BY QUADRICS - 374 11.2.3 SECANT ALGEBRAS OF MONOMIAL IDEALS - 377 11.2.4 RELATION TO STARLIKE LINEARITY - 378 11.2.5 HIGHER SECANTS ---- 380 11.3 EXCERPTS ON THE DIAGONAL IDEAL - 381 11.3.1 SYZYGIES AND DIMENSION ----- 382 11.3.2 THE LINEAR TYPE PROPERTY ----- 383 11.4 EXERCISES ---- 386 CONTENTS XV 12 ALUFFI ALGEBRAS - 389 12.1 RELATION TO CHERN CLASSES ----- 389 12.2 THE CASE OF IDEALS: EMBEDDED VERSION ---- 390 12.2.1 PRELIMINARIES ---- 390 12.2.2 DIMENSION ---- 392 12.2.3 TORSION AND MINIMAL PRIMES ----- 395 12.2.4 RELATION TO THE ARTIN-REES NUMBER ---- 398 12.2.5 SELECTED EXAMPLES ---- 402 12.2.6 THE ALUFFI ALGEBRA OF A GRADIENT IDEAL ---- 405 12.3 THE CASE OF MODULES ----- 407 12.3.1 THE EMBEDDED VERSION ----- 408 12.3.2 TAKING INVERSE LIMIT ----- 409 12.3.3 THE MODULE OF DERIVATIONS OF A POLYNOMIAL FORM ---- 413 12.3.4 THE NORMAL MODULE OF A PERFECT IDEAL OF CODIMENSION 2 ---- 421 12.4 EXERCISES ---- 427 BIBLIOGRAPHY---- 431 INDEX ---- 441
adam_txt	CONTENTS ACKNOWLEDGMENTS - VII FOREWORD - IX 1 1.1 1.2 1.2.1 1.2.2 1.3 1.4 GEOMETRIC MOTIVATION - 1 BITS FROM INTERSECTION THEORY - 1 CORRESPONDENCES AND INCIDENCE VARIETIES - 4 EXAMPLES ---- 4 ALGEBRAIC COUNTERPART - 6 RULED JOINS ---- 7 EXERCISES - 10 2 2.1 2.2 2.2.1 2.2.2 2.3 2.3.1 2.3.2 2.3.3 2.3.4 2.4 GRADED ALGEBRAS - 13 ARBITRARY GRADINGS - 13 NOTABLE BIGRADED ALGEBRAS - 16 THE SYMMETRIC ALGEBRA - 16 OTHER BIGRADED ALGEBRAS - 18 STANDARD GRADED ALGEBRAS - 18 REES ALGEBRAS OF IDEALS - 18 REES ALGEBRAS OF MODULES ---- 28 COMPLEMENTS ON THE FIBER CONE - 36 COHOMOLOGICAL INVARIANTS - 39 EXERCISES - 41 3 3.1 3.1.1 3.1.2 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.3 3.3.1 3.3.2 3.4 3.4.1 3.4.2 RATIONAL MAPS, 1 - 47 BASICS OF RATIONAL MAPS - 47 TERMINOLOGY - 47 BASIC PROPERTIES - 48 A CHARACTERISTIC-FREE CRITERION OF BIRATIONALITY - 50 PROLEGOMENA: THE KOSZUL-HILBERT LEMMA - 50 PRELIMINARIES ON RATIONAL MAPS ON REDUCED VARIETIES - 51 THE JACOBIAN DUAL RANK VERSUS BIRATIONALITY - 59 STATEMENT AND PROOF OF THE CRITERION - 63 A ROLE OF SYZYGIES ---- 67 BIRATIONAL COMBINATORICS - 70 THE UNDERLYING ARITHMETIC - 71 MONOMIAL BIRATIONAL MAPS IN DEGREE TWO - 73 ON THE DEGREE OF A RATIONAL MAP - 77 BASIC INGREDIENTS - 77 DEGREE UPPER BOUNDS - 81 XII CONTENTS 3.5 EXERCISES ----- 85 4 RATIONAL MAPS, II - 89 4.1 COMPLEMENTS ON THE BASE IDEAL ----89 4.1.1 DEGREE SEQUENCES - 89 4.1.2 THE SEMILINEAR RELATION TYPE ------92 4.2 INVERSION FACTORS OF BIRATIONAL MAPS ---- 93 4.2.1 BASIC LANDSCAPE ---- 94 4.2.2 RELATION TO SYMBOLIC POWERS ------- 96 4.3 NEWTON COMPLEMENTARY DUAL ------- 97 4.3.1 PRELIMINARIES ---- 97 4.3.2 MAIN RESULTS ---- 99 4.3.3 RELATION TO THE GRAPH OF A RATIONAL MAP ---- 104 4.4 ELEMENTS OF RATIONAL MAPS OVER A GROUND RING ---- 108 4.4.1 ALGEBRAIC DATA ---- 108 4.4.2 RATIONAL MAPS AND REPRESENTATIVES ----- 110 4.4.3 DEGREE UNDER SPECIALIZATION ---- 113 4.5 EXERCISES ---- 115 5 THE GRADIENT IDEAL - 119 5.1 THE UNDERLYING GEOMETRY ----- 119 5.1.1 LINEAR TYPE ---- 120 5.1.2 HYPERPLANE ARRANGEMENTS ---- 121 5.1.3 BEHAVIOR ALONG A FAMILY ----- 129 5.2 FREE DIVISORS ----- 140 5.2.1 GENERAL NONSENSE ---- 140 5.2.2 ALGEBRAIC LOGARITHMIC VECTOR FIELDS ----- 141 5.2.3 FAMILIES OF FREE DIVISORS ----- 145 5.2.4 WEIGHTED HOMOGENEOUS DIVISORS ---- 148 5.3 EXERCISES ----- 155 6 CREMONA TRANSFORMATIONS, I - 159 6.1 PLANE CREMONA TRANSFORMATIONS: HOMALOIDAL NETS ---- 159 6.1.1 WEIGHTED CLUSTER OF BASE POINTS ---- 159 6.1.2 RELATION TO FAT IDEALS ---- 163 6.1.3 FROM FAT IDEALS BACK TO THE CREMONA BASE IDEAL - 172 6.1.4 PROPER HOMALOIDAL TYPES WITH LARGE HIGHEST VIRTUAL MULTIPLICITY ---- 173 6.2 PLANE CREMONA TRANSFORMATIONS: SUBHOMALOIDAL TYPES - 179 6.2.1 ARITHMETIC QUADRATIC TRANSFORMATIONS ACTING ON FAT POINTS ---- 179 6.2.2 SUBHOMALOIDAL MULTIPLICITY SETS ----- 181 6.2.3 3-UNIFORM SUBHOMALOIDAL TYPES ----- 183 6.2.4 MAIN THEOREM ---- 199 CONTENTS - XIII 6.2.5 6.3 7 7.1 7.1.1 7.1.2 7.1.3 7.1.4 7.1.5 7.2 7.2.1 7.2.2 7.2.3 7.3 7.3.1 7.3.2 7.3.3 7.4 8 8.1 8.2 8.3 8.3.1 8.3.2 8.3.3 8.4 8.4.1 8.4.2 8.5 8.6 8.7 9 9.1 9.1.1 9.1.2 9.1.3 9.2 RELATION TO BORDIGA-WHITE PARAMETRIZATIONS ---- 203 EXERCISES ---- 206 CREMONA TRANSFORMATIONS, II - 209 GENERALIZED DE JONQUIERES TRANSFORMATIONS ---- 209 FULLY DOWNGRADED SEQUENCES - 211 GENERALIZED DE JONQUIERES TRANSFORMATIONS ---- 213 GENERALIZED DE JONQUIERES TRANSFORMATIONS UNDER NEWTON DUALITY ---- 215 GENERALIZED DE JONQUIERES TRANSFORMATIONS WITH IDENTITY SUPPORT ---- 218 THE MINIMAL FREE RESOLUTION OF THE BASE IDEAL ---- 218 THE GRAPH (BLOWUP) OF A CREMONA MAP ---- 220 THE GRAPH OF A DE JONQUIERES MAP WITH IDENTITY SUPPORT ---- 220 CREMONA MAPS WITH A COHEN-MACAULAY GRAPH ---- 227 CREMONA MAPS AND SYMBOLIC REES ALGEBRAS - 231 MONOMIAL CREMONA TRANSFORMATIONS ---- 235 THE GROUP OF MONOMIAL CREMONA TRANSFORMATIONS ---- 235 MONOMIAL CREMONA TRANSFORMATIONS OF DEGREE 2 ---- 243 A DUALITY PRINCIPLE ---- 256 EXERCISES ---- 259 STEPS IN ELIMINATION - 263 ELIMINATION ALGEBRAS ---- 263 IMPLICITIZATION ---- 266 DE JONQUIERES LIKE IMPLICITIZATION ---- 267 ALGEBRAIC PRELIMS ---- 267 THE (/F,G)-PARAMETRIZATION ---- 268 THE EQUATIONS OF THE REES ALGEBRA ---- 273 IMPLICITIZATION IN DIMENSION 1 ---- 278 DIMENSION ZERO ---- 278 DIMENSION ONE ---- 293 THE CLASSICAL RESULTANT ---- 295 ELIMINATING FROM CORRESPONDENCES ---- 297 EXERCISES ---- 300 THE GAUSS MAP - 303 GAUSS IMAGE OF HIGHER ORDER ---- 303 NOTABLE CASES. I: THE ORDINARY GAUSS IMAGE ---- 305 NOTABLE CASES. II: THE DUAL VARIETY ---- 306 RELATION TO THE TANGENTIAL VARIETY ---- 308 THE GAUSS IMAGE OF A UNIRATIONAL VARIETY ---- 310 XIV CONTENTS 9.2.1 THE ALGEBRAIC STRUCTURAL DATA - 310 9.2.2 THE GAUSS IMAGE OF TORIC VARIETIES ---- 313 9.2.3 ALGEBRAS OF VERONESE TYPE - 314 9.3 ABSTRACT GAUSS MAPS ---- 316 9.4 THE GEOMETRY OF THE ANALYTIC SPREAD ---- 317 9.4.1 MAXIMAL ANALYTIC SPREAD - 317 9.4.2 ANALYTIC SPREAD VERSUS THE FITTING IDEAL ---- 322 9.4.3 CASE STUDY: THE MODULE OF DIFFERENTIALS - 323 9.4.4 MAIN THEOREM OF ABSTRACT GAUSS MAPS ---- 325 9.5 EXERCISES ----- 329 10 TANGENT VARIETIES ---- 333 10.1 ALGEBRAIC FULTON-HANSEN THEOREMS ----- 333 10.1.1 ALGEBRAIC PRELIMINARIES - 333 10.1.2 THE UNDERLYING GEOMETRY ---- 337 10.1.3 THE TANGENTIAL VARIETY TO A UNIRATIONAL VARIETY - 340 10.2 REFINED PROPERTIES OF TANGENT ALGEBRAS - 341 10.2.1 EXPECTED STAR DIMENSION ---- 343 10.2.2 SET THEORETIC STARLIKE LINEARITY ----- 347 10.2.3 STARLIKE LINEARITY - 348 10.2.4 BEHAVIOR UNDER FLAT DEFORMATION - 351 10.2.5 A GLIMPSE OF THE BLOWUP OF THE KAHLER DIFFERENTIALS ---- 354 10.3 EXERCISES ----- 356 11 EMBEDDED JOINSAND SECANTS - 359 11.1 JOINS ---- 359 11.1.1 ALGEBRAIC SIDE ----- 359 11.1.2 THE GEOMETRIC BACKGROUND ----- 360 11.1.3 RELATION TO THE BAYER-MUMFORD DEFORMATION - 363 11.1.4 THE EMBEDDED JOIN OF A UNION OF LINEAR SPACES - 366 11.1.5 INITIAL DEGREE OF A JOIN - 368 11.2 SECANTS ----- 369 11.2.1 SECANTS OF DETERMINANTALAND PFAFFIAN SCHEMES - 370 11.2.2 SECANTS OFVARIETIES CUT BY QUADRICS - 374 11.2.3 SECANT ALGEBRAS OF MONOMIAL IDEALS - 377 11.2.4 RELATION TO STARLIKE LINEARITY - 378 11.2.5 HIGHER SECANTS ---- 380 11.3 EXCERPTS ON THE DIAGONAL IDEAL - 381 11.3.1 SYZYGIES AND DIMENSION ----- 382 11.3.2 THE LINEAR TYPE PROPERTY ----- 383 11.4 EXERCISES ---- 386 CONTENTS XV 12 ALUFFI ALGEBRAS - 389 12.1 RELATION TO CHERN CLASSES ----- 389 12.2 THE CASE OF IDEALS: EMBEDDED VERSION ---- 390 12.2.1 PRELIMINARIES ---- 390 12.2.2 DIMENSION ---- 392 12.2.3 TORSION AND MINIMAL PRIMES ----- 395 12.2.4 RELATION TO THE ARTIN-REES NUMBER ---- 398 12.2.5 SELECTED EXAMPLES ---- 402 12.2.6 THE ALUFFI ALGEBRA OF A GRADIENT IDEAL ---- 405 12.3 THE CASE OF MODULES ----- 407 12.3.1 THE EMBEDDED VERSION ----- 408 12.3.2 TAKING INVERSE LIMIT ----- 409 12.3.3 THE MODULE OF DERIVATIONS OF A POLYNOMIAL FORM ---- 413 12.3.4 THE NORMAL MODULE OF A PERFECT IDEAL OF CODIMENSION 2 ---- 421 12.4 EXERCISES ---- 427 BIBLIOGRAPHY---- 431 INDEX ---- 441
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id	DE-604.BV048488997
illustrated	Not Illustrated
index_date	2024-07-03T20:41:08Z
indexdate	2024-07-10T09:39:30Z
institution	BVB
institution_GND	(DE-588)10095502-2
isbn	9783110637540 3110637545
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-033866510
oclc_num	1310785505
open_access_boolean
owner	DE-634
owner_facet	DE-634
physical	XV, 445 Seiten 24 cm, 876 g
publishDate	2022
publishDateSearch	2022
publishDateSort	2022
publisher	De Gruyter
record_format	marc
series	De Gruyter expositions in mathematics
series2	De Gruyter expositions in mathematics
spelling	Simis, Aron 1942- Verfasser (DE-588)120670683X aut Graded algebras in algebraic geometry Aron Simis, Zaqueu Ramos Berlin De Gruyter [2022] XV, 445 Seiten 24 cm, 876 g txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics volume 70 Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Graduierter Ring (DE-588)4158003-5 gnd rswk-swf Graduierter Modul Graduierter Ring Kommutative Algebra Schnitt <Mathematik> Algebraische Geometrie Algebraische Geometrie (DE-588)4001161-6 s Kommutative Algebra (DE-588)4164821-3 s Graduierter Ring (DE-588)4158003-5 s DE-604 Ramos, Zaqueu Verfasser (DE-588)1264231784 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe Simis, Aron, 1942- Graded Algebras in Algebraic Geometry 1. Auflage Berlin/Boston : De Gruyter, 2022 Online-Ressource, 464 Seiten Erscheint auch als Online-Ausgabe 9783110640694 De Gruyter expositions in mathematics volume 70 (DE-604)BV004069300 70 X:MVB https://www.degruyter.com/isbn/9783110637540 B:DE-101 application/pdf https://d-nb.info/1245021982/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033866510&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p dnb 20220818 DE-101 https://d-nb.info/provenance/plan#dnb
spellingShingle	Simis, Aron 1942- Ramos, Zaqueu Graded algebras in algebraic geometry De Gruyter expositions in mathematics Algebraische Geometrie (DE-588)4001161-6 gnd Kommutative Algebra (DE-588)4164821-3 gnd Graduierter Ring (DE-588)4158003-5 gnd
subject_GND	(DE-588)4001161-6 (DE-588)4164821-3 (DE-588)4158003-5
title	Graded algebras in algebraic geometry
title_auth	Graded algebras in algebraic geometry
title_exact_search	Graded algebras in algebraic geometry
title_exact_search_txtP	Graded algebras in algebraic geometry
title_full	Graded algebras in algebraic geometry Aron Simis, Zaqueu Ramos
title_fullStr	Graded algebras in algebraic geometry Aron Simis, Zaqueu Ramos
title_full_unstemmed	Graded algebras in algebraic geometry Aron Simis, Zaqueu Ramos
title_short	Graded algebras in algebraic geometry
title_sort	graded algebras in algebraic geometry
topic	Algebraische Geometrie (DE-588)4001161-6 gnd Kommutative Algebra (DE-588)4164821-3 gnd Graduierter Ring (DE-588)4158003-5 gnd
topic_facet	Algebraische Geometrie Kommutative Algebra Graduierter Ring
url	https://www.degruyter.com/isbn/9783110637540 https://d-nb.info/1245021982/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033866510&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV004069300
work_keys_str_mv	AT simisaron gradedalgebrasinalgebraicgeometry AT ramoszaqueu gradedalgebrasinalgebraicgeometry AT walterdegruytergmbhcokg gradedalgebrasinalgebraicgeometry

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