Points and curves in the monster tower:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2010
|
| Series: | Memoirs of the American Mathematical Society
956 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 203, number 956 (end of volume)" Literaturverz. S. 135 - 136 |
| Physical Description: | IX, 137 S. |
| ISBN: | 9780821848180 |
Staff View
MARC
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| 245 | 1 | 0 | |a Points and curves in the monster tower |c Richard Montgomery ; Michail Zhitomirskii |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2010 | |
| 300 | |a IX, 137 S. | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 956 | |
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| 500 | |a Literaturverz. S. 135 - 136 | ||
| 650 | 4 | |a Blowing up (Algebraic geometry) | |
| 650 | 4 | |a Jet bundles (Mathematics) | |
| 650 | 4 | |a Pfaffian systems | |
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Record in the Search Index
| _version_ | 1804141065872080896 |
|---|---|
| adam_text | Contents
Preface
їх
Chapter
1.
Introduction
1
1.1.
The Monster construction
1
1.2.
Coordinates and the contact case
1
1.3.
Symmetries. Equivalence of points of the Monster
2
1.4.
Prolonging symmetries
2
1.5.
The basic theorem
2
1.6.
The Monster and Goursat distributions
3
1.7.
Our approach
4
1.8.
Proof of the basic theorem
5
1.9.
Plan of the paper
б
Acknowledgements
И
Chapter
2.
Prolongations of integral curves.
Regular, vertical, and critical curves and points
13
2.1.
From Monster curves to Legendrian curves
13
2.2.
Prolonging curves
13
2.3.
Projections and prolongations of local symmetries
15
2.4.
Proof of Theorem
2.2 15
2.5.
Erom
curves to points
16
2.6.
Non-singular points
17
2.7.
Critical curves
17
2.8.
Critical and regular directions and points
20
2.9.
Regular integral curves
20
2.10.
Régularisation
theorem
22
2.11.
An equivalent definition of a non-singular point
23
2.12.
Vertical and tangency directions and points
24
Chapter
3.
RVT classes. RVT codes of plane curves.
RVT and Puiseux
27
3.1.
Definition of RVT classes
27
3.2.
Two more definitions of a non-singular point
28
3.3.
Types of RVT classes. Regular and entirely critical prolongations
28
3.4.
Classification problem: reduction to regular RVT classes
29
3.5.
RVT classes as subsets of PfcM2
29
3.6.
Why tangency points?
30
3.7.
RVT code of plane curves
31
3.8.
RVT code and Puiseux characteristic
33
iii
iv CONTENTS
Chapter
4. Monsterization
and Legendrization.
Reduction theorems
39
4.1.
Definitions and basic properties
39
4.2.
Explicit calculation of the legendrization of RVT classes
41
4.3.
From points to Legendrian curves
42
4.4.
Simplest classification results
43
4.5.
On the implications and shortfalls of Theorems
4.14
and
4.15 44
4.6.
Prom points to Legendrian curve jets.
The jet-identification number
45
4.7.
The parameterization number
47
4.8.
Evaluating the jet-identification number
50
4.9.
Proof of Proposition
4.44 52
4.10.
From Theorem
В
to Theorem
4.40 53
4.11.
Proof that critical points do not have a jet-identification number
55
4.12.
Proof of Proposition
4.26 55
4.13.
Conclusions. Things to come
55
Chapter
5.
Reduction algorithm.
Examples of classification results
57
5.1.
Algorithm for calculating the Legendrization
and the parameterization number
57
5.2.
Reduction algorithm for the equivalence problem
59
5.3.
Reduction algorithm for the classification problem
60
5.4.
Classes of small codimension consisting of a finite number of orbits
61
5.5.
Classification of tower-simple points
53
5.6.
Classes of high codimension consisting of one or two orbits
67
5.7.
Further examples of classification results; Moduli
69
Chapter
6.
Determination of simple points
71
6.1.
Tower-simple and stage-simple points
71
6.2.
Determination theorems
71
6.3.
Explicit description of stage-simple RVT classes
74
6.4.
Local simplicity of RVT classes
79
6.5.
Proof of Theorem
6.4 81
6.6.
Proof of Theorem
6.6 82
6.7.
Proof of Theorem
6.30 83
Chapter
7.
Local coordinate systems on the Monster
85
7.1.
The KR coordinate system
85
7.2.
Critical curves in the KR coordinates
88
7.3.
RVT classes and KR coordinates
89
7.4.
Monsterization in KR coordinates
90
Chapter
8.
Prolongations and directional blow-up.
Proof of Theorems A and
В
95
8.1.
Directional blow-up and KR coordinates
96
8.2.
Directional blow-up and the maps
Et,
Ev,
L
99
8.3.
Proof of Theorem A for Puiseux characteristics
[λ0; λι]
100
8.4.
Further properties of the directional blow-up
101
8.5.
Proof of Theorem A for arbitrary Puiseux characteristics
104
CONTENTS v
8.6.
Proof of Theorem
В
of section
4.8 105
8.7.
Proof of Propositions
8.10
and
8.11 106
Chapter
9.
Open questions
109
9.1.
Unfolding versus prolongation.
109
9.2.
Prolongation
=
blow-up?
109
9.3.
Puiseux characteristic of Legendrian curves
113
9.4.
The infinite Monster
114
9.5.
Moduli and
projective
geometry
116
9.6.
RVT and the growth vector
116
Appendix A. Classification of integral
Engel
curves
119
Appendix B. Contact classification of Legendrian curves
123
B.I. Reduction theorems for curves
123
B.2. Reduction theorems for jets
124
B.3. Proof of Proposition
5.6,
part (i)
126
B.4. Proof of Proposition
5.6,
part (ii)
127
B.5. Proof of Proposition
5.5 127
Appendix C. Critical, singular and rigid curves
131
C.I. Critical
=φ·
locally rigid
131
C.2. Singular
==>·
critical
132
C.3. Another proof that vertical curves are rigid
133
Bibliography
135
Index
137
|
| any_adam_object | 1 |
| author | Montgomery, Richard 1956- Žitomirskij, Michail J. |
| author_GND | (DE-588)108222497 |
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| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | Montgomery, Richard 1956- Verfasser (DE-588)108222497 aut Points and curves in the monster tower Richard Montgomery ; Michail Zhitomirskii Providence, RI American Math. Soc. 2010 IX, 137 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 956 "Volume 203, number 956 (end of volume)" Literaturverz. S. 135 - 136 Blowing up (Algebraic geometry) Jet bundles (Mathematics) Pfaffian systems Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Pfaff-Differentialform (DE-588)4319094-7 gnd rswk-swf Aufblasung (DE-588)4139570-0 gnd rswk-swf Jetbündel (DE-588)4498250-1 gnd rswk-swf Vektorraumbündel (DE-588)4187470-5 gnd rswk-swf Vektorraumbündel (DE-588)4187470-5 s Jetbündel (DE-588)4498250-1 s Singularität Mathematik (DE-588)4077459-4 s DE-604 Aufblasung (DE-588)4139570-0 s Pfaff-Differentialform (DE-588)4319094-7 s Žitomirskij, Michail J. Verfasser aut Memoirs of the American Mathematical Society 956 (DE-604)BV008000141 956 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018930343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Montgomery, Richard 1956- Žitomirskij, Michail J. Points and curves in the monster tower Memoirs of the American Mathematical Society Blowing up (Algebraic geometry) Jet bundles (Mathematics) Pfaffian systems Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd Pfaff-Differentialform (DE-588)4319094-7 gnd Aufblasung (DE-588)4139570-0 gnd Jetbündel (DE-588)4498250-1 gnd Vektorraumbündel (DE-588)4187470-5 gnd |
| subject_GND | (DE-588)4077459-4 (DE-588)4319094-7 (DE-588)4139570-0 (DE-588)4498250-1 (DE-588)4187470-5 |
| title | Points and curves in the monster tower |
| title_auth | Points and curves in the monster tower |
| title_exact_search | Points and curves in the monster tower |
| title_full | Points and curves in the monster tower Richard Montgomery ; Michail Zhitomirskii |
| title_fullStr | Points and curves in the monster tower Richard Montgomery ; Michail Zhitomirskii |
| title_full_unstemmed | Points and curves in the monster tower Richard Montgomery ; Michail Zhitomirskii |
| title_short | Points and curves in the monster tower |
| title_sort | points and curves in the monster tower |
| topic | Blowing up (Algebraic geometry) Jet bundles (Mathematics) Pfaffian systems Singularities (Mathematics) Singularität Mathematik (DE-588)4077459-4 gnd Pfaff-Differentialform (DE-588)4319094-7 gnd Aufblasung (DE-588)4139570-0 gnd Jetbündel (DE-588)4498250-1 gnd Vektorraumbündel (DE-588)4187470-5 gnd |
| topic_facet | Blowing up (Algebraic geometry) Jet bundles (Mathematics) Pfaffian systems Singularities (Mathematics) Singularität Mathematik Pfaff-Differentialform Aufblasung Jetbündel Vektorraumbündel |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018930343&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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