On the shape of possible counterexamples to the Jacobian Conjecture

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

On the shape of possible counterexamples to the Jacobian Conjecture

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

Sección de Matemáticas

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

5 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	Español
Páginas (desde-hasta)	13-74
Número de páginas	62
Publicación	Journal of Algebra
Volumen	471
Estado	Publicada - 1 feb. 2017

Citar esto

@article{5cc986b0acd74fceae53e8df27b5daf2,

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.",

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

year = "2017",

month = feb,

day = "1",

language = "Espa{\~n}ol",

volume = "471",

pages = "13--74",

journal = "Journal of Algebra",

issn = "0021-8693",

}

TY - JOUR

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.

M3 - Artículo

SN - 0021-8693

VL - 471

SP - 13

EP - 74

JO - Journal of Algebra

JF - Journal of Algebra

ER -