Subgroups of polynomial automorphisms

Connell, E. H.; Zweibel, John

doi:10.1090/s0273-0979-1990-15944-0

Cited by 9 publications

(3 citation statements)

References 5 publications

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“…The Jacobian conjecture, raised by Keller [20], has been studied by many mathematicians: a partial list of related results includes [1,2,3,4,5,6,7,8,9,10,11,12,13,16,17,18,19,21,22,25,26,27,28,29,30,31,32]. A survey is given in [14,15].…”

Section: Introductionmentioning

confidence: 99%

On the two-dimensional Jacobian conjecture: Magnus' formula revisited, I

Hurst¹,

Lee²,

Li³

et al. 2022

Preprint

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Let K be an algebraically closed field of characteristic 0. When the Jacobian (∂f /∂x)(∂g/∂y) − (∂g/∂x)(∂f /∂y) is a constant for f, g ∈ K[x, y], Magnus' formula from [23] describes the relations between the homogeneous degree pieces f i 's and g i 's. We show a more general version of Magnus' formula and prove a special case of the two-dimensional Jacobian conjecture as its application.

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Section: Introductionmentioning

confidence: 99%

On the two-dimensional Jacobian conjecture: Magnus' formula revisited, I

Hurst¹,

Lee²,

Li³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The Jacobian conjecture, raised by Keller [29], has been studied by many mathematicians: a partial list of related results includes [3,1,4,5,6,7,14,8,10,11,12,13,15,16,19,23,26,27,30,32,38,39,41,43,44,50,51,52]. A survey is given in [17,18].…”

Section: Introductionmentioning

confidence: 99%

On the two-dimensional Jacobian conjecture: Magnus' formula revisited, II

Glidewell¹,

Hurst²,

Lee³

et al. 2022

Preprint

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This article is part of an ongoing investigation of the two-dimensional Jacobian conjecture. In the first paper of this series, we proved the generalized Magnus' formula. In this paper, inspired by cluster algebras, we introduce a sequence of new conjectures including the remainder vanishing conjecture. This makes the generalized Magnus' formula become a useful tool to show the two-dimensional Jacobian conjecture. In the forthcoming paper(s), we plan to prove the remainder vanishing conjecture.

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“…By linear change of variables, we can assume that f dn = x and g dn = y. The case of n = 2, where (1.1) is trivially satisfied, has been proved in [2], [6,Corollary 6], [8], [16], [20] for the plane case under the assumption are the only ones that contribute to the coefficient…”

Section: Introductionmentioning

confidence: 99%