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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Detalles Bibliográficos
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
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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.

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