Automorphisms of affine spaces: proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF)
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1995
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 243 S. graph. Darst. |
| ISBN: | 0792335236 |
Staff View
MARC
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| 245 | 1 | 0 | |a Automorphisms of affine spaces |b proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF) |c ed. by Arno van den Essen |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
DIRECTOR S PREFACE xi
FOREWORD xiii
SCIENTIFIC PROGRAM xv
Workshop xv
Conference xvi
Participants xvii
I Polynomial Maps in Dimension n 1
SEVEN LECTURES ON POLYNOMIAL
AUTOMORPHISMS 3
Arno van den Essen
1 Lecture. Invertible polynomial maps; a first encounter ... 3
2 Lecture. The Jacobian Conjecture 8
3 Lecture. An invertibility criterion 15
4 Lecture. The tame generators problem 20
5 Lecture. Invertible polynomial maps and algebraic group
actions 24
5.1 The Linearization Problem 26
5.2 The Fixed Point problem 26
5.3 The Cancelation Problem 27
6 Lecture. The kernel of a derivation 28
7 Lecture. Why should you believe the Jacobian Conjecture? 32
8 Acknowledgments 36
THE JACOBIAN CONJECTURE:
SOME STEPS TOWARDS SOLUTION 41
Ludwik Druzkowski
1 Formulation of the Jacobian Conjecture 41
2 Basic facts on polynomial mappings 42
3 The Jacobian Conjecture in C2 44
4 Reduction of the degree 45
5 Global asymptotic stability problem and the real Jacobian
Problem 46
6 Inversion formulas 49
v
vi
FINITE AUTOMORPHISMS OF AFFINE N SPACE 55
Hanspeter Kraft and Gerald Schwarz
1 Introduction 56
2 The amalgamated product structure of AutA2 56
3 Non linearizable group actions and G vector bundles .... 58
4 The equivariant SERRE Problem for abelian groups 61
POLYOMORPHISMS CONJUGATE TO DILATIONS 67
Gary Meisters
1 Background and terminology 67
2 What s in this paper Proposition 2.1 68
3 Proof of Proposition 2.1 69
4 Kernel matrices A for cubic linear maps 73
5 Two cubic linear maps showing /, / 1, hs and h~l .... 74
6 Rusek s Example Other Non cubic linear Examples ... 75
6.1 Degree 6 7 Schroder terms for Rusek s 2D 75
6.2 Reduction of 2D Rusek to 5D cubic homogeneous . . 76
7 Another cubic homogeneous but not cubic linear 78
8 Conjectures: What seems to be true 79
9 The Poincare Siegel Theory 80
A Nelson s example, Anick s example Reduction of Degree . 81
A.I Nelson s Example of The Poincare Siegel Theory . . 81
A.2 Anick s 4D cubic homogeneous non triangularizable 82
A.3 Reduction Algorithm 84
ON SEPARABLE ALGEBRAS OVER A U.F.D. AND THE
JACOBIAN CONJECTURE IN ANY CHARACTERISTIC 89
Kossivi Adjamagbo
1 On the transfer of separability from an algebra to a sub algebra 90
2 Isomorphism theorems for algebras over a U.F.D 99
3 Application to the Jacobian conjecture 101
GLOBAL INJECTIVITY OF POLYNOMIAL MAPS VIA
VECTOR FIELDS 105
Anna Cima, Armengol Gasull, Jaume LLibre and Francesc Manosas
1 Introduction and statement of the results 105
2 Proof of Theorem 1.2 108
3 Proof of Theorem 1.3 113
4 Proof of Theorem 1.4 118
5 On the Markus Yamabe Conjecture 119
Scientific Program vii
II Two dimensional Results 125
ON THE MARKUS YAMABE CONJECTURE 127
Robert Fefiler
1 Introduction 127
2 History of the Markus Yamabe Conjecture 127
3 Relation to the Jacobian Conjecture 129
4 Solution of the two dimensional Markus Yamabe Conjecture 129
DERIVATIONS GENERATED BY POLYNOMIALS,
THEIR IMAGES AND COMPLEMENTS OF THE
IMAGES 137
Yosef Stein
1 Review of recent results 137
2 Some new results 140
3 Miscellaneous questions 144
NORMAL FORMS AND THE JACOBIAN
CONJECTURE 145
David Wright
1 Introduction 145
2 Connection with the Jacobian Conjecture 146
3 The Intermediate Ring U 146
4 Specific Coset Representatives 147
5 Preparation Theorems 149
6 Integrality and Exactness 151
7 Reformulation of the Two Dimensional Jacobian Conjecture 153
8 Further Observations on the Case t = 3 154
RADIAL SIMILARITY OF NEWTON POLYGONS 157
Charles Cheng and Stuart Wang
AN ALGORITHM THAT DETERMINES WHETHER
A POLYNOMIAL MAP IS BIJECTIVE 169
Charles Cheng and Stuart Wang
1 Introduction 169
2 Determining K[f,g] = K[t] 169
3 Determining Automorphisms 171
4 Decomposing Automorphisms 173
viii
III Group Actions 177
ALGEBRAIC ASPECTS OF ADDITIVE GROUP ACTIONS
ON COMPLEX AFFINE SPACE 179
James Deveney and David Finston
1 Rational Triangulability 179
2 Rings of Ga Invariants 182
3 Proper versus Locally Trivial Ga Actions 183
4 Locally Trivial vs Equivariantly Trivial Actions 186
5 Free Ga Actions on C3 188
QUOTIENTS OF ALGEBRAIC GROUP ACTIONS 191
Harm Derksen
1 Introduction 191
2 Examples of quotients 191
3 Properties of actions 194
4 A counterexample 196
ONE PARAMETER SUBGROUPS AND THE TRIANGULAR
SUBGROUP OF THE AFFINE CREMONA GROUP 201
Gene Freudenburg
1 One Parameter Subgroups 202
1.1 Locally Nilpotent Derivations 202
1.2 Rank and Triangulability 203
1.3 Facts about Kernels 207
2 Resolving Triangular Automorphisms in Dimension 3 .... 208
A NOTE ON NAGATA S AUTOMORPHISM 215
Jacques Alev
1 Introduction 215
2 The tameness problem and Nagata s automorphism 215
3 The main observation 217
IV Reactions on the conference 223
ON A QUESTION OF YOSEF STEIN 225
Hanspeter Kraft
A COUNTEREXAMPLE TO A CONJECTURE OF
MEISTERS 231
Arno van den Essen
1 The counterexample 231
Scientific Program ix
2 Meisters Conjecture holds if n 3 232
3 Acknowledgment 233
Appendix 235
OPEN PROBLEMS 237
SOME CONFERENCE IMPRESSIONS 241
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| genre_facet | Konferenzschrift 1994 Curaçao |
| id | DE-604.BV010525969 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:54:29Z |
| institution | BVB |
| isbn | 0792335236 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007015476 |
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| physical | XIX, 243 S. graph. Darst. |
| publishDate | 1995 |
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| spelling | Automorphisms of affine spaces proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF) ed. by Arno van den Essen Dordrecht [u.a.] Kluwer 1995 XIX, 243 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Automorphismus (DE-588)4143709-3 gnd rswk-swf Affiner Raum (DE-588)4141574-7 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1994 Curaçao gnd-content Affiner Raum (DE-588)4141574-7 s Automorphismus (DE-588)4143709-3 s DE-604 Essen, Arnoldus R. van den Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007015476&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Automorphisms of affine spaces proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF) Automorphismus (DE-588)4143709-3 gnd Affiner Raum (DE-588)4141574-7 gnd |
| subject_GND | (DE-588)4143709-3 (DE-588)4141574-7 (DE-588)1071861417 |
| title | Automorphisms of affine spaces proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF) |
| title_auth | Automorphisms of affine spaces proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF) |
| title_exact_search | Automorphisms of affine spaces proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF) |
| title_full | Automorphisms of affine spaces proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF) ed. by Arno van den Essen |
| title_fullStr | Automorphisms of affine spaces proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF) ed. by Arno van den Essen |
| title_full_unstemmed | Automorphisms of affine spaces proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF) ed. by Arno van den Essen |
| title_short | Automorphisms of affine spaces |
| title_sort | automorphisms of affine spaces proceedings of a conference held in curacao netherlands antilles july 4 8 1994 under auspices of the caribbean mathematical foundation cmf |
| title_sub | proceedings of a conference held in Curaçao (Netherlands Antilles), July 4 - 8, 1994, under auspices of the Caribbean Mathematical Foundation (CMF) |
| topic | Automorphismus (DE-588)4143709-3 gnd Affiner Raum (DE-588)4141574-7 gnd |
| topic_facet | Automorphismus Affiner Raum Konferenzschrift 1994 Curaçao |
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