Desingularization: invariants and strategy: application to dimension 2
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Cham
Springer
[2020]
|
| Series: | Lecture notes in mathematics
2270 |
| Subjects: | |
| Online Access: | Cover Buchcover Inhaltsverzeichnis |
| Physical Description: | viii, 256 Seiten Diagramme |
| ISBN: | 9783030526399 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Vincent Cossart • Uwe Jannsen • Shuji Saito
Desingularization: Invariants
and Strategy
Application to Dimension 2
With Contributions by Bernd Schober
Springer
Contents
1 Introduction 1
1 1 Whal Is Desingularization? 1
1 2 Very Short History of Desingularization 2
1 3 How Did we Start? 3
1 4 Summary 4
1 5 Conventions and Concluding Remarks 13
2 Basic Invariants for Singularities 15
2 1 Invariants of Graded Rings and Homogeneous Ideals in
Polynomial Rings 15
2 2 Invariants for Local Rings 21
2 3 Invariants for Schemes 25
3 Permissible Blow-Ups 37
4 8-Permissible Blow-Ups: The Embedded Case 49
5 B-Permissible Blow-Ups: The Non-embedded Case 65
6 Main Theorems and Strategy for Their Proofs 79
7 (u)-standard Bases 105
8 Characteristic Polyhedra of JCR 117
9 Transformation of Standard Bases Under Blow-Ups 133
10 Termination of the Fundamental Sequences of B-Permissible
Blow-Ups, and the Case ex (X) = 1 145
11 Additional Invariants in the Case ex(X) = 2 155
12 Proof in the Case ez(X) = esx(X) = 2,1: Some Key Lemmas 161
13 Proof in the Case ex(X) = ex(X) = 2, II: Separable Residue
Extensions 167
vii
Contents
viii
14 Proof in the Case ex(X) = e, (X) = 2, HI: Inseparable Residue
Extensions 175
15 Non-existence of Maximal Contact in Dimension 2 191
16 An Alternative Proof of Theorem 6 17 201
17 Functoriality, Locally Noetherian Schemes, Algebraic Spaces
and Stacks 205
18 Appendix by B Schober: Hironaka’s Characteristic
Polyhedron Notes for Novices 211
18 1 Introduction 211
18 2 The Newton Polyhedron of an Ideal 216
18 3 The Projected Polyhedron and Its Relation to the Newton
Polyhedron 221
18 4 The Directrix and Its Role: Choosing («) 228
18 5 Determining the Characteristic Polyhedron: Optimizing the
Choice of (/; y) 233
18 6 Invariants from the Polyhedron and the Effect of Blowing Up_ 238
References 249
|
| adam_txt |
Vincent Cossart • Uwe Jannsen • Shuji Saito
Desingularization: Invariants
and Strategy
Application to Dimension 2
With Contributions by Bernd Schober
Springer
Contents
1 Introduction 1
1 1 Whal Is Desingularization? 1
1 2 Very Short History of Desingularization 2
1 3 How Did we Start? 3
1 4 Summary 4
1 5 Conventions and Concluding Remarks 13
2 Basic Invariants for Singularities 15
2 1 Invariants of Graded Rings and Homogeneous Ideals in
Polynomial Rings 15
2 2 Invariants for Local Rings 21
2 3 Invariants for Schemes 25
3 Permissible Blow-Ups 37
4 8-Permissible Blow-Ups: The Embedded Case 49
5 B-Permissible Blow-Ups: The Non-embedded Case 65
6 Main Theorems and Strategy for Their Proofs 79
7 (u)-standard Bases 105
8 Characteristic Polyhedra of JCR 117
9 Transformation of Standard Bases Under Blow-Ups 133
10 Termination of the Fundamental Sequences of B-Permissible
Blow-Ups, and the Case ex (X) = 1 145
11 Additional Invariants in the Case ex(X) = 2 155
12 Proof in the Case ez(X) = esx(X) = 2,1: Some Key Lemmas 161
13 Proof in the Case ex(X) = ex(X) = 2, II: Separable Residue
Extensions 167
vii
Contents
viii
14 Proof in the Case ex(X) = e, (X) = 2, HI: Inseparable Residue
Extensions 175
15 Non-existence of Maximal Contact in Dimension 2 191
16 An Alternative Proof of Theorem 6 17 201
17 Functoriality, Locally Noetherian Schemes, Algebraic Spaces
and Stacks 205
18 Appendix by B Schober: Hironaka’s Characteristic
Polyhedron Notes for Novices 211
18 1 Introduction 211
18 2 The Newton Polyhedron of an Ideal 216
18 3 The Projected Polyhedron and Its Relation to the Newton
Polyhedron 221
18 4 The Directrix and Its Role: Choosing («) 228
18 5 Determining the Characteristic Polyhedron: Optimizing the
Choice of (/; y) 233
18 6 Invariants from the Polyhedron and the Effect of Blowing Up_ 238
References 249 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T15:31:03Z |
| indexdate | 2024-07-10T08:57:31Z |
| institution | BVB |
| isbn | 9783030526399 |
| language | English |
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| physical | viii, 256 Seiten Diagramme |
| publishDate | 2020 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Cossart, Vincent Verfasser (DE-588)1218545216 aut Desingularization: invariants and strategy application to dimension 2 Vincent Cossart, Uwe Jannsen, Shuji Saito ; with contributions by Bernd Schober Cham Springer [2020] viii, 256 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2270 Auflösung von Singularitäten (DE-588)4181537-3 gnd rswk-swf Auflösung von Singularitäten (DE-588)4181537-3 s DE-604 Jannsen, Uwe 1954- Verfasser (DE-588)141967870 aut Saito, Shuji 1957- Verfasser (DE-588)1025836103 aut Schober, Bernd (DE-588)1218545496 ctb Erscheint auch als Online-Ausgabe 978-3-030-52640-5 Erscheint auch als Online-Ausgabe 9783030526405 Lecture notes in mathematics 2270 (DE-604)BV000676446 2270 V:DE-576;X:SPRINGER image/jpeg http://swbplus.bsz-bw.de/bsz1728597161cov.htm 20200917175848 Cover SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032329538&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Buchcover HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032329538&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cossart, Vincent Jannsen, Uwe 1954- Saito, Shuji 1957- Desingularization: invariants and strategy application to dimension 2 Lecture notes in mathematics Auflösung von Singularitäten (DE-588)4181537-3 gnd |
| subject_GND | (DE-588)4181537-3 |
| title | Desingularization: invariants and strategy application to dimension 2 |
| title_auth | Desingularization: invariants and strategy application to dimension 2 |
| title_exact_search | Desingularization: invariants and strategy application to dimension 2 |
| title_exact_search_txtP | Desingularization: invariants and strategy application to dimension 2 |
| title_full | Desingularization: invariants and strategy application to dimension 2 Vincent Cossart, Uwe Jannsen, Shuji Saito ; with contributions by Bernd Schober |
| title_fullStr | Desingularization: invariants and strategy application to dimension 2 Vincent Cossart, Uwe Jannsen, Shuji Saito ; with contributions by Bernd Schober |
| title_full_unstemmed | Desingularization: invariants and strategy application to dimension 2 Vincent Cossart, Uwe Jannsen, Shuji Saito ; with contributions by Bernd Schober |
| title_short | Desingularization: invariants and strategy |
| title_sort | desingularization invariants and strategy application to dimension 2 |
| title_sub | application to dimension 2 |
| topic | Auflösung von Singularitäten (DE-588)4181537-3 gnd |
| topic_facet | Auflösung von Singularitäten |
| url | http://swbplus.bsz-bw.de/bsz1728597161cov.htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032329538&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032329538&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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