Some families of polynomial automorphisms III

• Eric Edo ^[1] ; Drew Lewis ^[2]
  1. [1] University of New Caledonia

     University of New Caledonia

     Nueva Caledonia

     
  2. [2] University of Alabama, (USA)
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 4 ((April 2015) ), 2015, págs. 864-874
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.05.023
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• Resumen

  • We prove that the closure (for the Zariski topology) of the set of polynomial automorphisms of the complex affine plane whose polydegree is (cd−1,b,a)(cd−1,b,a) contains all automorphisms of polydegree (cd+a)(cd+a) where a,b≥2a,b≥2 and c≥1c≥1 are integers and d=ab−1d=ab−1. When b=2b=2, this result gives a family of counterexamples to a conjecture of Furter.