On the shape of possible counterexamples to the Jacobian Conjecture

Christian Valqui; Jorge A. Guccione; Juan J. Guccione

doi:10.1016/j.jalgebra.2016.08.039

On the shape of possible counterexamples to the Jacobian Conjecture

Christian Valqui
, Jorge A. Guccione
, Juan J. Guccione

Sección de Matemáticas

Instituto de Matemática y Ciencias Afines
Universidad de Buenos Aires
Pabellón 1-Ciudad Universitaria
Consejo Nacional de Investigaciones Científicas y Técnicas

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

9 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	13-74
Número de páginas	62
Publicación	Journal of Algebra
Volumen	471
DOI	https://doi.org/10.1016/j.jalgebra.2016.08.039
Estado	Publicada - 1 feb. 2017

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title = "On the shape of possible counterexamples to the Jacobian Conjecture",

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.",

keywords = "Jacobian Conjecture, Minimal counterexample",

author = "Christian Valqui and Guccione, \{Jorge A.\} and Guccione, \{Juan J.\}",

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doi = "10.1016/j.jalgebra.2016.08.039",

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T1 - On the shape of possible counterexamples to the Jacobian Conjecture

AU - Valqui, Christian

AU - Guccione, Jorge A.

AU - Guccione, Juan J.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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.

KW - Jacobian Conjecture

KW - Minimal counterexample

UR - https://www.scopus.com/pages/publications/84988847930

U2 - 10.1016/j.jalgebra.2016.08.039

DO - 10.1016/j.jalgebra.2016.08.039

M3 - Article

AN - SCOPUS:84988847930

SN - 0021-8693

VL - 471

SP - 13

EP - 74

JO - Journal of Algebra

JF - Journal of Algebra

ER -

On the shape of possible counterexamples to the Jacobian Conjecture

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