Artículo
Valqui, C.; Guccione, J.A.; Guccione, J.J. "On the shape of possible counterexamples to the Jacobian Conjecture" (2017) Journal of Algebra. 471:13-74
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Abstract:
We improve the algebraic methods of Abhyankar for the Jacobian Conjecture in dimension two and describe the shape of possible counterexamples. We give an elementary proof of the result of Heitmann in [5], which states that gcd(deg(P),deg(Q))≥16 for any counterexample (P,Q). We also prove that gcd(deg(P),deg(Q))≠2p for any prime p. © 2016 Elsevier Inc.
Registro:
| Documento: | Artículo |
| Título: | On the shape of possible counterexamples to the Jacobian Conjecture |
| Autor: | Valqui, C.; Guccione, J.A.; Guccione, J.J. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, UBA, Pabellón 1 – Ciudad Universitaria, Intendente Guiraldes 2160, Buenos Aires, C1428EGA, Argentina Instituto de Investigaciones Matemáticas “Luis A. Santaló”, Facultad de Ciencias Exactas y Naturales, UBA, Pabellón 1 – Ciudad Universitaria, Intendente Guiraldes 2160, Buenos Aires, C1428EGA, Argentina Instituto Argentino de Matemática – CONICET, Saavedra 15 3er piso, Buenos Aires, C1083ACA, Argentina Pontificia Universidad Católica del Perú, Sección Matemáticas, PUCP, Av. Universitaria 1801, San Miguel, Lima, 32, Peru Instituto de Matemática y Ciencias Afines (IMCA), Calle Los Biólogos 245, Urb San César, La Molina, Lima, 12, Peru |
| Palabras clave: | Jacobian Conjecture; Minimal counterexample |
| Año: | 2017 |
| Volumen: | 471 |
| Página de inicio: | 13 |
| Página de fin: | 74 |
| DOI: | http://dx.doi.org/10.1016/j.jalgebra.2016.08.039 |
| Título revista: | Journal of Algebra |
| Título revista abreviado: | J. Algebra |
| ISSN: | 00218693 |
| CODEN: | JALGA |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v471_n_p13_Valqui |
Referencias:
- Abhyankar, S.S., Lectures on Expansion Techniques in Algebraic Geometry (1977) Tata Institute of Fundamental Research Lectures on Mathematics and Physics, 57. , Tata Institute of Fundamental Research Bombay notes by Balwant Singh, MR542446 (80m:14016)
- Abhyankar, S.S., Some thoughts on the Jacobian Conjecture, Part II (2008) J. Algebra, 319, pp. 1154-1248
- Abhyankar, S.S., Some thoughts on the Jacobian Conjecture. III (2008) J. Algebra, 320, pp. 2720-2826
- Guccione, J.A., Guccione, J.J., Valqui, C., The Dixmier conjecture and the shape of possible counterexamples (2014) J. Algebra, 399, pp. 581-633
- Heitmann, R., On the Jacobian conjecture (1990) J. Pure Appl. Algebra, 64, pp. 35-72. , MR1055020 (91c:14018)
- Joseph, A., The Weyl algebra – semisimple and nilpotent elements (1975) Amer. J. Math., 97, pp. 597-615. , MR0379615 (52:520)
- Keller, O.-H., Ganze Cremona-Transformationen (1939) Monatsh. Math. Phys., 47 (1), pp. 299-306. , (German). MR1550818
- Lang, J., Jacobian pairs. II (1991) J. Pure Appl. Algebra, 74 (1), pp. 61-71. , MR1129130 (92k:14015)
- Moh, T.T., On the Jacobian conjecture and the configurations of roots (1983) J. Reine Angew. Math., 340, pp. 140-212. , MR691964 (84m:14018)
- (2013), On the Newton polygon of a Jacobian mate, Max-Planck-Institut für Mathematik Preprint Series (53); van den Essen, A., Polynomial automorphisms and the Jacobian conjecture (2000) Progress in Mathematics, 190. , Birkhäuser Verlag Basel MR1790619 (2001j:14082)
- Zoladek, H., An application of Newton–Puiseux charts to the Jacobian problem (2008) Topology, 47, pp. 431-469. , MR2427734 (2009h:14108)
Citas:
---------- APA ----------
Valqui, C., Guccione, J.A. & Guccione, J.J. (2017) . On the shape of possible counterexamples to the Jacobian Conjecture. Journal of Algebra, 471, 13-74.http://dx.doi.org/10.1016/j.jalgebra.2016.08.039
---------- CHICAGO ----------
Valqui, C., Guccione, J.A., Guccione, J.J. "On the shape of possible counterexamples to the Jacobian Conjecture" . Journal of Algebra 471 (2017) : 13-74.http://dx.doi.org/10.1016/j.jalgebra.2016.08.039
---------- MLA ----------
Valqui, C., Guccione, J.A., Guccione, J.J. "On the shape of possible counterexamples to the Jacobian Conjecture" . Journal of Algebra, vol. 471, 2017, pp. 13-74.http://dx.doi.org/10.1016/j.jalgebra.2016.08.039
---------- VANCOUVER ----------
Valqui, C., Guccione, J.A., Guccione, J.J. On the shape of possible counterexamples to the Jacobian Conjecture. J. Algebra. 2017;471:13-74.http://dx.doi.org/10.1016/j.jalgebra.2016.08.039
