On the shape of possible counterexamples to the Jacobian Conjecture

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...

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Autores principales: Valqui, C., Guccione, J.A., Guccione, J.J.
Formato: JOUR
Materias:
Jacobian Conjecture
Minimal counterexample
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00218693_v471_n_p13_Valqui
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00218693_v471_n_p13_Valqui2023-10-03T14:21:34Z On the shape of possible counterexamples to the Jacobian Conjecture Valqui, C. Guccione, J.A. Guccione, J.J. Jacobian Conjecture Minimal counterexample 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. Fil:Guccione, J.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Guccione, J.J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00218693_v471_n_p13_Valqui
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Jacobian Conjecture
Minimal counterexample
spellingShingle Jacobian Conjecture
Minimal counterexample
Valqui, C.
Guccione, J.A.
Guccione, J.J.
On the shape of possible counterexamples to the Jacobian Conjecture
topic_facet Jacobian Conjecture
Minimal counterexample
description 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.
format JOUR
author Valqui, C.
Guccione, J.A.
Guccione, J.J.
author_facet Valqui, C.
Guccione, J.A.
Guccione, J.J.
author_sort Valqui, C.
title On the shape of possible counterexamples to the Jacobian Conjecture
title_short On the shape of possible counterexamples to the Jacobian Conjecture
title_full On the shape of possible counterexamples to the Jacobian Conjecture
title_fullStr On the shape of possible counterexamples to the Jacobian Conjecture
title_full_unstemmed On the shape of possible counterexamples to the Jacobian Conjecture
title_sort on the shape of possible counterexamples to the jacobian conjecture
url http://hdl.handle.net/20.500.12110/paper_00218693_v471_n_p13_Valqui
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