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Points and curves in the Monster tower / / Richard Montgomery, Michail Zhitomirskii
| Points and curves in the Monster tower / / Richard Montgomery, Michail Zhitomirskii |
| Autore | Montgomery R (Richard), <1956-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (137 p.) |
| Disciplina | 516.3/6 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Jet bundles (Mathematics)
Blowing up (Algebraic geometry) Pfaffian systems Singularities (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0570-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Preface""; ""Chapter 1. Introduction""; ""1.1. The Monster construction""; ""1.2. Coordinates and the contact case""; ""1.3. Symmetries. Equivalence of points of the Monster""; ""1.4. Prolonging symmetries""; ""1.5. The basic theorem""; ""1.6. The Monster and Goursat distributions""; ""1.7. Our approach""; ""1.8. Proof of the basic theorem""; ""1.9. Plan of the paper""; ""Acknowledgements""; ""Chapter 2. Prolongations of integral curves. Regular, vertical, and critical curves and points ""; ""2.1. From Monster curves to Legendrian curves""
""2.2. Prolonging curves""""2.3. Projections and prolongations of local symmetries""; ""2.4. Proof of Theorem 2.2""; ""2.5. From curves to points""; ""2.6. Non-singular points""; ""2.7. Critical curves""; ""2.8. Critical and regular directions and points""; ""2.9. Regular integral curves""; ""2.10. Regularization theorem""; ""2.11. An equivalent definition of a non-singular point""; ""2.12. Vertical and tangency directions and points""; ""Chapter 3. RVT classes. RVT codes of plane curves. RVT and Puiseux""; ""3.1. Definition of RVT classes"" ""3.2. Two more definitions of a non-singular point""""3.3. Types of RVT classes. Regular and entirely critical prolongations""; ""3.4. Classification problem: reduction to regular RVT classes""; ""3.5. RVT classes as subsets of PkR2 ""; ""3.6. Why tangency points?""; ""3.7. RVT code of plane curves""; ""3.8. RVT code and Puiseux characteristic""; ""Chapter 4. Monsterization and Legendrization. Reduction theorems""; ""4.1. Definitions and basic properties""; ""4.2. Explicit calculation of the legendrization of RVT classes""; ""4.3. From points to Legendrian curves"" ""4.4. Simplest classification results""""4.5. On the implications and shortfalls of Theorems 4.14 and 4.15""; ""4.6. From points to Legendrian curve jets. The jet-identification number ""; ""4.7. The parameterization number""; ""4.8. Evaluating the jet-identification number""; ""4.9. Proof of Proposition 4.44""; ""4.10. From Theorem B to Theorem 4.40""; ""4.11. Proof that critical points do not have a jet-identification number""; ""4.12. Proof of Proposition 4.26""; ""4.13. Conclusions. Things to come""; ""Chapter 5. Reduction algorithm. Examples of classification results"" ""5.1. Algorithm for calculating the Legendrization and the parameterization number""""5.2. Reduction algorithm for the equivalence problem""; ""5.3. Reduction algorithm for the classification problem""; ""5.4. Classes of small codimension consisting of a finite number of orbits""; ""5.5. Classification of tower-simple points""; ""5.6. Classes of high codimension consisting of one or two orbits""; ""5.7. Further examples of classification results; Moduli""; ""Chapter 6. Determination of simple points""; ""6.1. Tower-simple and stage-simple points""; ""6.2. Determination theorems"" ""6.3. Explicit description of stage-simple RVT classes"" |
| Record Nr. | UNINA-9910481011703321 |
Montgomery R (Richard), <1956->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Points and curves in the Monster tower / / Richard Montgomery, Michail Zhitomirskii
| Points and curves in the Monster tower / / Richard Montgomery, Michail Zhitomirskii |
| Autore | Montgomery R (Richard), <1956-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (137 p.) |
| Disciplina | 516.3/6 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Jet bundles (Mathematics)
Blowing up (Algebraic geometry) Pfaffian systems Singularities (Mathematics) |
| ISBN | 1-4704-0570-9 |
| Classificazione | SI 130 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Preface""; ""Chapter 1. Introduction""; ""1.1. The Monster construction""; ""1.2. Coordinates and the contact case""; ""1.3. Symmetries. Equivalence of points of the Monster""; ""1.4. Prolonging symmetries""; ""1.5. The basic theorem""; ""1.6. The Monster and Goursat distributions""; ""1.7. Our approach""; ""1.8. Proof of the basic theorem""; ""1.9. Plan of the paper""; ""Acknowledgements""; ""Chapter 2. Prolongations of integral curves. Regular, vertical, and critical curves and points ""; ""2.1. From Monster curves to Legendrian curves""
""2.2. Prolonging curves""""2.3. Projections and prolongations of local symmetries""; ""2.4. Proof of Theorem 2.2""; ""2.5. From curves to points""; ""2.6. Non-singular points""; ""2.7. Critical curves""; ""2.8. Critical and regular directions and points""; ""2.9. Regular integral curves""; ""2.10. Regularization theorem""; ""2.11. An equivalent definition of a non-singular point""; ""2.12. Vertical and tangency directions and points""; ""Chapter 3. RVT classes. RVT codes of plane curves. RVT and Puiseux""; ""3.1. Definition of RVT classes"" ""3.2. Two more definitions of a non-singular point""""3.3. Types of RVT classes. Regular and entirely critical prolongations""; ""3.4. Classification problem: reduction to regular RVT classes""; ""3.5. RVT classes as subsets of PkR2 ""; ""3.6. Why tangency points?""; ""3.7. RVT code of plane curves""; ""3.8. RVT code and Puiseux characteristic""; ""Chapter 4. Monsterization and Legendrization. Reduction theorems""; ""4.1. Definitions and basic properties""; ""4.2. Explicit calculation of the legendrization of RVT classes""; ""4.3. From points to Legendrian curves"" ""4.4. Simplest classification results""""4.5. On the implications and shortfalls of Theorems 4.14 and 4.15""; ""4.6. From points to Legendrian curve jets. The jet-identification number ""; ""4.7. The parameterization number""; ""4.8. Evaluating the jet-identification number""; ""4.9. Proof of Proposition 4.44""; ""4.10. From Theorem B to Theorem 4.40""; ""4.11. Proof that critical points do not have a jet-identification number""; ""4.12. Proof of Proposition 4.26""; ""4.13. Conclusions. Things to come""; ""Chapter 5. Reduction algorithm. Examples of classification results"" ""5.1. Algorithm for calculating the Legendrization and the parameterization number""""5.2. Reduction algorithm for the equivalence problem""; ""5.3. Reduction algorithm for the classification problem""; ""5.4. Classes of small codimension consisting of a finite number of orbits""; ""5.5. Classification of tower-simple points""; ""5.6. Classes of high codimension consisting of one or two orbits""; ""5.7. Further examples of classification results; Moduli""; ""Chapter 6. Determination of simple points""; ""6.1. Tower-simple and stage-simple points""; ""6.2. Determination theorems"" ""6.3. Explicit description of stage-simple RVT classes"" |
| Record Nr. | UNINA-9910788857503321 |
|
Montgomery R (Richard), <1956->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Points and curves in the Monster tower / / Richard Montgomery, Michail Zhitomirskii
| Points and curves in the Monster tower / / Richard Montgomery, Michail Zhitomirskii |
| Autore | Montgomery R (Richard), <1956-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
| Descrizione fisica | 1 online resource (137 p.) |
| Disciplina | 516.3/6 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Jet bundles (Mathematics)
Blowing up (Algebraic geometry) Pfaffian systems Singularities (Mathematics) |
| ISBN | 1-4704-0570-9 |
| Classificazione | SI 130 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Abstract""; ""Preface""; ""Chapter 1. Introduction""; ""1.1. The Monster construction""; ""1.2. Coordinates and the contact case""; ""1.3. Symmetries. Equivalence of points of the Monster""; ""1.4. Prolonging symmetries""; ""1.5. The basic theorem""; ""1.6. The Monster and Goursat distributions""; ""1.7. Our approach""; ""1.8. Proof of the basic theorem""; ""1.9. Plan of the paper""; ""Acknowledgements""; ""Chapter 2. Prolongations of integral curves. Regular, vertical, and critical curves and points ""; ""2.1. From Monster curves to Legendrian curves""
""2.2. Prolonging curves""""2.3. Projections and prolongations of local symmetries""; ""2.4. Proof of Theorem 2.2""; ""2.5. From curves to points""; ""2.6. Non-singular points""; ""2.7. Critical curves""; ""2.8. Critical and regular directions and points""; ""2.9. Regular integral curves""; ""2.10. Regularization theorem""; ""2.11. An equivalent definition of a non-singular point""; ""2.12. Vertical and tangency directions and points""; ""Chapter 3. RVT classes. RVT codes of plane curves. RVT and Puiseux""; ""3.1. Definition of RVT classes"" ""3.2. Two more definitions of a non-singular point""""3.3. Types of RVT classes. Regular and entirely critical prolongations""; ""3.4. Classification problem: reduction to regular RVT classes""; ""3.5. RVT classes as subsets of PkR2 ""; ""3.6. Why tangency points?""; ""3.7. RVT code of plane curves""; ""3.8. RVT code and Puiseux characteristic""; ""Chapter 4. Monsterization and Legendrization. Reduction theorems""; ""4.1. Definitions and basic properties""; ""4.2. Explicit calculation of the legendrization of RVT classes""; ""4.3. From points to Legendrian curves"" ""4.4. Simplest classification results""""4.5. On the implications and shortfalls of Theorems 4.14 and 4.15""; ""4.6. From points to Legendrian curve jets. The jet-identification number ""; ""4.7. The parameterization number""; ""4.8. Evaluating the jet-identification number""; ""4.9. Proof of Proposition 4.44""; ""4.10. From Theorem B to Theorem 4.40""; ""4.11. Proof that critical points do not have a jet-identification number""; ""4.12. Proof of Proposition 4.26""; ""4.13. Conclusions. Things to come""; ""Chapter 5. Reduction algorithm. Examples of classification results"" ""5.1. Algorithm for calculating the Legendrization and the parameterization number""""5.2. Reduction algorithm for the equivalence problem""; ""5.3. Reduction algorithm for the classification problem""; ""5.4. Classes of small codimension consisting of a finite number of orbits""; ""5.5. Classification of tower-simple points""; ""5.6. Classes of high codimension consisting of one or two orbits""; ""5.7. Further examples of classification results; Moduli""; ""Chapter 6. Determination of simple points""; ""6.1. Tower-simple and stage-simple points""; ""6.2. Determination theorems"" ""6.3. Explicit description of stage-simple RVT classes"" |
| Record Nr. | UNINA-9910827647103321 |
|
Montgomery R (Richard), <1956->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||