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Polynomial automorphisms and the Jacobian conjecture : new results from the beginning of the 21st Century / / A. R. P. van den Essen, Shigeru Kuroda, Anthony J. Crachiola
| Polynomial automorphisms and the Jacobian conjecture : new results from the beginning of the 21st Century / / A. R. P. van den Essen, Shigeru Kuroda, Anthony J. Crachiola |
| Autore | Essen A. R. P. van den (Arnoldus Richardus Petrus van den), <1951-> |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (197 pages) : illustrations |
| Disciplina | 516.35 |
| Collana | Frontiers in Mathematics |
| Soggetto topico |
Automorphisms
Jacobi polynomials Automorfismes |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-60535-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466389403316 |
Essen A. R. P. van den (Arnoldus Richardus Petrus van den), <1951->
|
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| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Polynomial Automorphisms and the Jacobian Conjecture : New Results from the Beginning of the 21st Century / / by Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola
| Polynomial Automorphisms and the Jacobian Conjecture : New Results from the Beginning of the 21st Century / / by Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola |
| Autore | Essen A. R. P. van den (Arnoldus Richardus Petrus van den), <1951-> |
| Edizione | [1st ed. 2021.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2021 |
| Descrizione fisica | 1 online resource (197 pages) : illustrations |
| Disciplina | 516.35 |
| Collana | Frontiers in Mathematics |
| Soggetto topico |
Geometry, Algebraic
Algebra Mathematics Algebraic Geometry Automorfismes |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-60535-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgments -- Contents -- 1 The Shestakov-Umirbaev Theory and Nagata's Conjecture -- 1.1 The Shestakov-Umirbaev Theory -- 1.1.1 Nagata's Conjecture -- 1.1.2 Weighted Grading -- 1.1.3 Initial Algebras and Elementary Reductions -- 1.1.4 Wildness Criterion -- 1.2 Structure of the Proof -- 1.2.1 Key Propositions -- 1.2.2 Induction -- 1.2.3 Proof of Claim A -- 1.2.4 Proof of Claim B -- Summary of Sect.1.2 -- 1.3 Degree Inequalities -- 1.3.1 Differentials -- 1.3.2 Shestakov-Umirbaev Inequality -- 1.3.3 Useful Consequences -- 1.3.4 Exercises -- 1.3.5 Degrees of Cofactor Expansions -- 1.4 Weak Shestakov-Umirbaev Condition -- 1.4.1 Description of g1 and g2 -- 1.4.2 Degree Estimations -- 1.5 Completion of the Proof -- 1.6 How to Find Reductions -- 1.6.1 Elementary Reduction -- 1.6.2 Shestakov-Umirbaev Reduction -- 2 Counterexamples to Hilbert's Fourteenth Problem -- 2.1 Introduction -- 2.2 Main Theorem -- 2.2.1 Construction -- 2.2.2 A Sufficient Condition on t2,...,tn -- 2.2.3 Example and Remarks -- 2.3 Criterion for Non-finite Generation -- 2.4 Proof of Theorem 2.2.4, Part I -- 2.5 Proof of Theorem 2.2.4, Part II -- 2.6 Application (1): Derivations -- 2.7 Application (2): Invariant Fields -- 3 Prime Characteristic Methods and the Cancellation Problem -- 3.1 The Makar-Limanov and Derksen Invariants -- 3.2 Exponential Maps -- 3.3 Cancellation in Dimensions One and Two -- 3.4 Cancellation in Dimensions Three and Higher -- 4 The Jacobian Conjecture: New Equivalences -- 4.1 Preliminaries: Exterior Forms -- 4.2 The Canonical Poisson Algebra and the Poisson Conjecture -- 4.3 The Weyl Algebra and the Dixmier Conjecture -- Applications to the Case that R is a Domain -- 4.4 The Equivalence of the Dixmier, Jacobian, and Poisson Conjectures -- 4.5 A p-Adic Formulation of the Jacobian Conjecture and the Unimodular Conjecture -- Transitivity.
Keller Maps and the Unimodular Conjecture -- The Unimodular Conjecture over Zp -- 4.6 A Mysterious Faulty Proof of the Jacobian Conjecture -- 5 Mathieu-Zhao Spaces -- 5.1 Generalizing the Jacobian Conjecture -- 5.2 Mathieu-Zhao Spaces: Definition and Examples -- 5.3 Zhao's Idempotency Theorem -- 5.4 Orthogonal Polynomials and MZ-Spaces -- Orthogonal Polynomials -- 5.5 The Duistermaat-van der Kallen Theorem -- Polytopes -- The Density Theorem -- Applications of the Density Theorem -- Generalizing the Duistermaat-van der Kallen Theorems -- 5.6 The Generalized Vanishing Conjecture -- 5.7 The Image Conjecture -- 5.8 MZ-Spaces of Matrices of Codimension One -- Some Corrections to E1 -- Bibliography -- Index. |
| Record Nr. | UNINA-9910484880603321 |
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Essen A. R. P. van den (Arnoldus Richardus Petrus van den), <1951->
|
||
| Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Polynomial Rings and Affine Algebraic Geometry [[electronic resource] ] : PRAAG 2018, Tokyo, Japan, February 12−16 / / edited by Shigeru Kuroda, Nobuharu Onoda, Gene Freudenburg
| Polynomial Rings and Affine Algebraic Geometry [[electronic resource] ] : PRAAG 2018, Tokyo, Japan, February 12−16 / / edited by Shigeru Kuroda, Nobuharu Onoda, Gene Freudenburg |
| Edizione | [1st ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Descrizione fisica | 1 online resource (X, 315 p. 11 illus., 3 illus. in color.) |
| Disciplina | 512.4 |
| Collana | Springer Proceedings in Mathematics & Statistics |
| Soggetto topico |
Algebraic geometry
Commutative algebra Commutative rings Group theory Algebraic Geometry Commutative Rings and Algebras Group Theory and Generalizations |
| ISBN | 3-030-42136-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Ciliberto, C. and Zaidenberg, M: On Fano schemes of complete intersections -- Daigle, D.: Locally nilpotent sets of derivations -- DeBondt, M. and Watanabe, J: On the theory of Gordan-Noether on homogeneous forms with zero Hessian -- Dubouloz, A. and Petitijean, C: Rational real algebraic models of compact differential surfaces with circle actions -- Freudenburg, G.: The super-rank of a locally nilpotent derivation of a polynomial ring -- Gurjar, R., Masuda, K., and Miyanishi, M: Affine space fibrations -- Gurjar, R.: A graded domain is determined at its vertex: Applications to invariant theory -- Kojima, H.: Singularities of normal log canonical del Pezzo surfaces of rank one -- Moser-Jauslin, L.: O2(C)-vector bundles and equivariant real circle actions -- Nagamine, T.: On some sufficient conditions for polynomials to be closed polynomials over Domains -- Popov, V.: Variations on the theme of Zariski’s Cancellation Problem -- Takeda, Y.: Tango structures on curves in characteristic 2 -- Tanimoto, R.: Exponential matrices of size five-by-five -- Van den Essen, A.: Mathieu-Zhao Spaces and the Jacobian Conjecture. |
| Record Nr. | UNISA-996418269203316 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Polynomial Rings and Affine Algebraic Geometry : PRAAG 2018, Tokyo, Japan, February 12−16 / / edited by Shigeru Kuroda, Nobuharu Onoda, Gene Freudenburg
| Polynomial Rings and Affine Algebraic Geometry : PRAAG 2018, Tokyo, Japan, February 12−16 / / edited by Shigeru Kuroda, Nobuharu Onoda, Gene Freudenburg |
| Edizione | [1st ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Descrizione fisica | 1 online resource (X, 315 p. 11 illus., 3 illus. in color.) |
| Disciplina | 512.4 |
| Collana | Springer Proceedings in Mathematics & Statistics |
| Soggetto topico |
Geometry, Algebraic
Commutative algebra Commutative rings Group theory Algebraic Geometry Commutative Rings and Algebras Group Theory and Generalizations |
| ISBN | 3-030-42136-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Ciliberto, C. and Zaidenberg, M: On Fano schemes of complete intersections -- Daigle, D.: Locally nilpotent sets of derivations -- DeBondt, M. and Watanabe, J: On the theory of Gordan-Noether on homogeneous forms with zero Hessian -- Dubouloz, A. and Petitijean, C: Rational real algebraic models of compact differential surfaces with circle actions -- Freudenburg, G.: The super-rank of a locally nilpotent derivation of a polynomial ring -- Gurjar, R., Masuda, K., and Miyanishi, M: Affine space fibrations -- Gurjar, R.: A graded domain is determined at its vertex: Applications to invariant theory -- Kojima, H.: Singularities of normal log canonical del Pezzo surfaces of rank one -- Moser-Jauslin, L.: O2(C)-vector bundles and equivariant real circle actions -- Nagamine, T.: On some sufficient conditions for polynomials to be closed polynomials over Domains -- Popov, V.: Variations on the theme of Zariski’s Cancellation Problem -- Takeda, Y.: Tango structures on curves in characteristic 2 -- Tanimoto, R.: Exponential matrices of size five-by-five -- Van den Essen, A.: Mathieu-Zhao Spaces and the Jacobian Conjecture. |
| Record Nr. | UNINA-9910484645903321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||